Using performance reference compounds to compare mass transfer calibration methodologies in passive samplers deployed in the water column

Abstract

Performance reference compounds (PRCs) are often added to passive samplers prior to field deployments to provide information about mass transfer kinetics between the sampled environment and the passive sampler. Their popularity has resulted in different methods of varying complexity to estimate mass transfer and better estimate freely dissolved concentrations (C_free) of targeted compounds. Three methods for describing a mass transfer model are commonly used: a first order (FO) kinetic method, a non-linear least squares (NLS) fitting of sampling rate, and a diffusion (DIF) method. PRC-loaded, low-density polyethylene (PE) strips of four different thicknesses were used as passive samplers to create an array of PRC results to assess the comparability and reproducibility of each of the methods. Samplers were deployed in the water column at three stations in New Bedford Harbor (MA, USA). Collected data allowed C_free comparisons to be performed in two ways: (1) comparing C_free derived from one thickness using different methods and (2) comparing C_free derived by the same method using different thicknesses of PE. Overall, the NLS and DIF methods demonstrated the most precise results for all of the PCBs measured and generated C_free values that were often statistically indistinguishable. Relative standard deviations (RSDs) for total PCB measurements using the same thickness and varying model types range from 0.04–12% and increased with sampler thickness and RSDs for estimates using the same method and varying thickness ranged from 8 – 18%. Environmental scientists and managers are encouraged to use these methods when estimating C_free from passive sampling and PRC data.

Graphical Abstract

Mean freely dissolved water concentration (C_free) per PCB conger as measured without PRC correction and by each examined PRC modeling approach for a 76 ¼m thick LDPE passive sampler deployed in the water column of New Bedford Harbor.

INTRODUCTION

Passive sampling in environmental applications has evolved from a scientific concept to a tool being promoted for use in regulatory decision making (Greenberg et al., 2014, Booij et al., 2016, Mayer et al., 2003). During this evolution, several review articles have summarized the scientific foundations and approaches for passive sampling including its ability to estimate a chemical’s freely dissolved concentration (C_free)(Lohmann, 2012, Lydy et al., 2014, Mayer et al., 2014, Ghosh et al., 2014). The importance of C_free as a surrogate for a chemical’s actual bioavailable concentrations was described by (Di Toro et al., 1991) but measuring or estimating C_free in the water column or sediment interstitial waters can be challenging because of experimental artifacts (e.g., presence of colloids and dissolved organic carbon) and modeling uncertainties. Several studies have demonstrated the advantages of using passive sampling compared to traditional sampling and modelling approaches for measuring C_free (Gschwend et al., 2011, Burgess et al., 2015, Maruya et al., 2009). Using passive sampling to estimate C_free, environmental managers can make better informed decisions with greater certainty about the magnitude of risk associated with target contaminants at contaminated sites.

Ideally, when using passive sampling to measure C_free in the water column or sediment interstitial waters a thermodynamic equilibrium between the sampling environment and passive sampler is attained for all targeted contaminants. This equilibrium allows for the use of Equation 1 for calculating C_free (ng/L):

$$C_{free}=\frac{C_{PS}^{\infty }}{K_{PW}}$$ (1)

where, $C_{PS}^{\infty }\left(\text{ng}/{\text{kg}}_{\text{polymer}}\right)$is the concentration of a target contaminant in the passive sampler at equilibrium and K_PW (L_water/kg_polymer) is its polymer-water partition coefficient. In some instances, the application of the passive samplers requires ‘real world’ scenarios to be assessed and exposures must be performed in the field where environmental conditions may control the rate at which equilibrium is attained (Fernandez et al., 2014). In this respect, highly hydrophobic organic contaminants (HOCs) of interest may require months or even years to reach equilibrium. Assuming equilibrium has been attained and using Equation 1 to calculate C_free may result in under-estimating C_free and ultimately under-estimating exposure and risk for many hydrophobic compounds that have not reached equilibrium. In these cases, the use of performance reference compounds (PRCs) allows C_free to be estimated from the measured passive sampler concentration at a given time, $C_{PS}^t$(ng/kg_polymer), even when a compound has not attained equilibrium (Huckins et al., 2002). PRCs are dosed into a passive sampler prior to deployment and their release from the sampler can then be used to determine mass transfer kinetics to more accurately estimate C_free. Several methods, of varying complexity, describing this mass transfer have been developed to generate practical information about equilibrium conditions using PRC data.

The availability of multiple methods for estimating C_free using PRC data allows environmental scientists and managers options for assessing risk. The objective of this investigation was to generate a data set of target contaminant concentrations, estimate C_free using three different methods to model mass transfer, and compare the results. Low-density polyethylene (PE) in four thicknesses was used as a passive sampler and the target contaminants were 27 polychlorinated biphenyl (PCB) congeners. The deployment was performed in the water column of three stations at the New Bedford Harbor Superfund site in New Bedford, Massachusetts (USA).

From an environmental management perspective, the goal of this research is to provide guidance to environmental managers and scientists at contaminated sediment sites for selecting which method(s) to use when analyzing PRC data from passive sampling deployments.

Theory

The dominating environmental factor controlling sampling kinetics in the water column is the water boundary layer (WBL). The WBL is the region separating the passive sampler from the bulk water where molecular diffusion dictates mass transfer and resistance to mass transfer. HOCs are often rate limited by diffusion through the WBL when using PE as a sampling medium (Tomaszewski and Luthy, 2008, Belles et al., 2016, Vrana and Schüürmann, 2002). When kinetics are WBL-controlled there are several methods to estimate C_free using PRCs pre-loaded into a passive sampler. The simplest method for estimating C_free is using the release rate of PRCs based on first order kinetics which assumes that uptake into the passive sampler follows a first order (FO) kinetic regime as described by:

$$C_{free}=\frac{C_{PS}^t}{K_{PW}\cdot \left(1-e^{-k_{e}t}\right)}$$ (2)

where, t (days) is the deployment time and k_e(days⁻¹) is the overall exchange rate constant. The value for is determined from the fraction of PRC retained by the sampler, f_ret, over the course of the deployment:

$$k_e=-\left(\frac{\ln \left(\frac{c_{PRC}^t}{c_{PRC}^0}\right)}{t}\right)$$ (3)

where, $C_{PRC}^0$and $C_{PRC}^t$ (ng/kg_polymer) are the PRC concentrations in the PE prior to deployment and after deployment, respectively, this ratio defines f_ret. Often there is a specific PRC for each targeted HOC in the study (Joyce et al., 2015), though has been interpolated for target HOCs by correlation with K_OW, molecular volume, or molecular weight when a dedicated PRC was not used (Friedman et al., 2012, Perron et al., 2013a, Perron et al., 2013b). Because of analytical issues associated with low f_ret (i.e., quantification limit issues for low K_OW PRCs) and high f_ret (i.e., difficulty differentiating $C_{PRC}^0$ and $C_{PRC}^t$ of high K_OW PRCs), the literature suggests limiting the use of the f_ret to 0.2 < f_ret< 0.8, sometimes referred to as the 80/20 method (Smedes, 2007, Booij and Smedes, 2010).

Taking the mass transfer model one step further and calculating a sampling rate, R_S (L/day), introduces physiochemical characteristics of the PRCs and target compounds such that predictive relationships between all PRC data can be used to estimate compound specific sampling rates for targeted compounds. (Booij and Smedes, 2010) reported a method for better estimating R_S using a non-linear least squares (NLS) fit:

$$f_{ret}=e{}^{-R_s\cdot t}/{}_{m_p\cdot K_{PW}}$$ (4)

where m_p is the mass (kg) of the passive sampler and R_S is the product of m_p, K_PW, and k_e. It allows for using all acquired PRC data – even data for which the fraction of PRC retained by the passive sampler is less than 0.20 or greater than 0.8. This formula gives a site-specific R_S, guidance in calculating compound specific can be found in the literature(Booij and Smedes, 2010, Rusina et al., 2010). Once a compound specific R_S has been determined, C_free can be estimated from:

$$C_{free}=\raisebox{1ex}{$C_{PS}^t\cdot m_p$}\!\left/ \!\raisebox{-1ex}{$R_S\cdot t$}\right.$$ (5)

A third method for modelling mass transfer has also been developed for both the sediments and the water column and accounts for compound-specific diffusivities within both the sampler and the WBL or interstitial water (Fernandez et al., 2009, Fernandez et al., 2012, Apell and Gschwend, 2014, Thompson et al., 2015). The diffusion method (DIF) is useful when uptake is controlled or partially controlled by the polymer, or if it is unclear how a compound’s diffusion through the polymer will affect transfer kinetics. The model, derivation, and code used in this study were originally reported by (Thompson et al., 2015). It is based on Fickian diffusion in a symmetrical system with PE thickness (cm) of 2l and WBL of thickness b where x = 0 is the center of the PE film. Diffusion is assumed to be unidirectional through half the sheet thickness. The resulting governing equations for the system become:

$$\frac{\partial C_{PS}}{\partial t}=D_{PE}\frac{{\partial }^2{C}_{PS}}{\partial x^2}\text{−for}0<x<l$$ (6)

$$\frac{\partial C_{WBL}}{\partial t}=D_W\frac{{\partial }^2{C}_{WBL}}{\partial x^2}\text{ for }l<x<l+b$$ (7)

where, D_PE and D_W are the diffusivities (¼m²/s) of each HOC through the PE and water, respectively, x is the distance from the center of the PE, l is half the thickness of the PE (¼m), and b is the thickness of the WBL (¼m). Solving this system of partial differential equations allows for a calculation of the WBL thickness using PRC results. Assuming that compounds with varying physio-chemical properties experience the same WBL, data from several PRCs can be used to estimate an average WBL thickness though similar f_ret restrictions to the FO method must be implemented into the input. Once WBL thickness is known, fractional equilibriums (f_eq), can be estimated for target HOCs. For clarification, the f_eq refers to the fraction of equilibrium that had been attained by a target contaminant over the deployment period. It is related to the f_ret in that the sum of f_eq and f_ret should be one for a target contaminant and its corresponding PRC. Once f_eq are calculated for the target compounds, C_free can then be calculated as:

$$C_{free}=\left(\frac{c_{PS}^t}{f_{eq}}\right)/K_{PW}$$ (8)

The error associated with C_free can be attributed to different factors depending on the method used to estimate equilibrium conditions. In general, the error is mainly dependent on K_PW. Log K_PW values usually have an error of ±0.2 which can affect the calculated C_free by a factor of two. This work used an estimated set of log K_PW based on a log K_OW values (Ghosh et al., 2014, Hawker and Connell, 1988), as such K_PW would contribute to the systematic error of C_free estimates. For compounds near equilibrium, K_PW will be the dominant contributor to error and as the $C_{PRC}^t/C_{PRC}^0$ ratio gets smaller, analytical errors in these measurements will have a larger contribution to total error. When compounds are not at equilibrium, the K_PW and analytical error can amplify the error in C_free. For instance, error is introduced to the FO method because this method only uses one PRC for each targeted compound, whereas the NLS and DIF methods use data from all PRCs which should average-out analytical errors introduced by calculating $\frac{C_{PRC}^t}{C_{PRC}^0}$. In this way, errors introduced by K_{PW, $C_{PRC}^t,\text{ and }{C}_{PRC}^0$}contribute to total error differently depending on how close to equilibrium a compound is. As such, errors contributed by K_PW in C_free for Equations 1,2, and 8 would only contribute a bias between the C_free values from the different thicknesses tested. However, because K_PW is used to determine R_S, errors in K_PW will contribute to the final C_free generated by the NLS method, similar errors associated with D_W and D_PS will contribute to C_free error using the DIF method. These factors will likely contribute more toward bias and not variability. Much of the variability from the equilibrium corrections will be introduced through analytical error associated with$C_{PRC}^t,\text{ and }{C}_{PRC}^0$.

MATERIALS AND METHODS

Materials

Four different thicknesses of low-density PE sheeting (Ace Hardware, Oak Brook, IL, USA; 12.5 ¼m, 25.4 μm, 50.8¼m, and 76.2 ¼m thick) were cut into strips (8cm x 50cm, ~ 0.5 to 3 g) and pre-cleaned in dichloromethane (DCM; 1 day), methanol (MeOH; 2 days), and stored in ultrapure water (18.3 MΩ) prior to loading PRCs. Passive samplers were separated according to thickness. PRCs were loaded into cleaned PE in 2 L of a 4:1 MeOH:water spiking solution containing ¹³C-labeled PCB congeners: 8, 28, 52, 101, 138, and 180 (99%, Cambridge Isotope Laboratories, Inc., Andover, MA, USA) for 36 days while gently shaking on an orbital shaker. The nominal concentration of each PRC in the spiking solution is given in Table S1. PRC-loaded PE strips were then dried and woven on stainless steel wire (Malin Co., Brookpark, OH, USA; 20 gauge) which was then shaped into a ring. Prior to weaving on the wire, a piece of PE (~5 cm) was cut from each sampler to determine$C_{PE}^0$. Samplers were stored at −20 °C or on ice in the dark until deployment.

The target compounds of interest included 27 chlorinated biphenyls (CBs): 8, 18, 28, 44, 52, 66, 70, 77, 81, 99, 101, 105, 110, 114, 118, 123, 126, 138, 153, 156, 157, 167, 169, 170, 180, 189, and 206. Standards for non-labeled target PCBs (Ultra Scientific, North Kingston, RI, USA) were purchased individually, combined, and diluted in hexane to make a 3000 ng/mL stock standard solution. Internal standard, CB198, was also purchased from Ultra Scientific and recovery standards, ¹³C-PCB: 9, 118, and 188, were acquired from Cambridge Isotope Laboratories, Inc. ACS/Pesticide grade DCM and MeOH, were purchased from Honeywell (Muskegon, MI, USA) and used without further purification. Ultra-resi analysed grade hexane (95% n-hexane) was purchased from J.T. Baker (Center Valley, PA, USA). Concentrated sulfuric acid (Fisher Scientific, Hampton, NH, USA) was used to clean-up extracts when necessary.

Field studies

In September of 2014, all thicknesses of PE were deployed for 30 days, in triplicate, at two stations in New Bedford Harbor (NBH 2 and NBH4) and one station in Buzzards Bay (NBH5) (Figure S1). One non-PRC-loaded PE of each thickness was exposed to air during deployment and retrieval operations at each station to serve as a station-specific travel/field blank. One PRC-loaded PE blank of each thickness was also exposed but not deployed at all three stations and served as a travel/field blank. Upon retrieval, PE samplers were placed in aluminum foil and stored on ice during transit. Once at the laboratory, samplers were wiped clean of visible residue/biological growth using a lab tissue and rinsed with de-ionized water. Samplers were then dried and individually stored in pre-cleaned glass vials at −20°C in the dark until extraction.

Sample processing and analysis

PE samplers and blanks were spiked with recovery standards: ¹³Clabeled PCB 9, 118, and 188 (12.5 ¼L; 20 ¼g/mL) and extracted three times by gently mixing on an orbital shaker in DCM (~90mL, overnight). The combined DCM extract was concentrated using a TurboVap (Zymark, Hopkinton, MA, USA; 5–10 psi, 35°C), exchanged to hexane, and further concentrated to 0.5 mL. The TurboVap vial was then rinsed with an additional 0.5 mL of hexane and combined with the concentrated extract for 1 mL total volume. Internal standard, CB198 (12.5 ¼L; 20 ¼g/mL), was then added to the extract. Concentrated extracts from Stations NBH4 and NBH5 were dark green and therefore were acid washed with concentrated H₂SO₄ (200 ¼L) and allowed to separate overnight. The organic solvent layer was then pipetted off and stored. All sampler extracts were stored in amber glass, crimp cap vials at −20 °C in the dark until analysis by GC-MS (details in Supporting Information).

Data analysis and quality control

Chromatograms were integrated using MSD ChemStation (E.02.00.493; Santa Clara, CA, USA) and quantified by the internal standard method using a seven-point calibration curve. Analysis of pre-cleaned, virgin PE showed that no target contaminants were detectable prior to deployment. Six of the 5-cm, pre-cut pieces per thickness were extracted to determine $C_{PRC}^0$ for all PRCs, $C_{PRC}^0$values for each PRC agreed within 15%. One 76 ¼m thick PE replicate was lost during analysis, thus only duplicates were available. Throughout this paper, data are presented as the mean ± one standard deviation, unless otherwise stated. Recoveries of ¹³C-PCB 9, 118, and 188 were 51±9, 83±7, and 76± 6, respectively, for all PE at all three stations. All target contaminants were corrected for surrogate recovery according to Table S2. C_free was calculated using a compound specific K_PW (Table S2) and corrected for nonequilibrium conditions using the correction methods described in the Theory section. To compare PCB congener and total PCB C_free values generated by different thicknesses and method, analysis of variance (ANOVA) was performed followed by a protected Fisher’s test to identify any statistically-significant differences between method estimates of C_free. An α = 0.05 was used to indicate significant differences between mean C_free values. Analyses were performed using SAS 9.4 (Cary, NC, USA).

RESULTS AND DISCUSSION

Comparisons of the C_free generated by the different methods were performed in two ways: comparing C_free from different thicknesses of PE using the same correction method and comparing C_free from the same thickness using a different correction method. Similar concentration trends were observed at each sampling station. Comparisons from NBH2 will be shown in the main text and corresponding tables and figures for NBH4 and NBH5 are provided in the Supporting Information. All C_free values are given in Supporting Information (Tables S3 - S5). C_free results using equation 1 are reported, and compared, labeled as “no model” to illustrate the differences when equilibrium is assumed to be achieved.

PRC results

As expected, f_ret increased with increasing PRC log K_OW as well as with increasing PE thickness (Figure 1). PRC fraction retained was lowest at NBH5, followed by NBH2 and highest at NBH4 (Table S6). In most cases, small variations were observed between a station’s triplicates. However, in some instances, substantial variability was observed, so calculations of k_e, R_s, and WBL thickness (Table S7) were performed for each replicate as opposed to taking a mean for each station. The retention of the PRCs, ¹³C-PCB 8 and ¹³C-PCB 28, on the 25.4 ¼m thick PE was higher than expected at all stations and on all replicates. The ¹³C-PCB 8 results had a small influence on the resulting C_free calculations which can be observed in the elevated C_free concentration of CB8 using the FO method. The ¹³C-PCB 28 results had more variation as evidenced in both the FO and DIF model. The origins of this behavior are unclear but this behavior was consistent for all deployed PE. There was no indication of contamination in either the laboratory blanks or non-PRC loaded field blanks, and full scan data was not available due to their low concentrations. There was no evidence that these results were incorrect and they were used when applicable. All estimated f_eq values are given in Supporting Information Table S8.

Figure 1.

Performance reference compound (PRC) fraction retained (f_ret) from the deployment of four thicknesses of polyethylene passive samplers at station NBH2. PRCs are ¹³C-labelled PCB 8, 28, 52, 101, 138 and 180. The f_ret values are plotted against log K_OW of the PRCs.

Intra-method comparison of congener C_free

PRCs suggested that CB8 had reached equilibrium for all PE deployed. Calculating C_free using Equation 1 for all PE yielded approximately 20% relative standard deviation (RSD; Figure 2). This RSD was also observed at the NBH4 station for CB8 (Figure S4) suggesting that a 20% RSD would be representative of the precision for passive sampling in this investigation and served as a standard for good agreement for congeners where an equilibrium correction was appropriate. (Apell and Gschwend, 2016) came to a similar conclusion finding an estimated PE sampler RSD precision of 27%.

Figure 2.

Relative standard deviation (RSD; n = 12) of C_free values for all four thicknesses at station NBH2 measured with a given equilibrium model: (1) No model, (2) first order kinetic (FO) method, (3) non-linear least squared (NLS) sampling rate method, and (4) Diffusion (DIF) method. The designations (e.g., ‘Di’, ‘Tri’, ‘Tetra’) indicate the chlorination level of congeners along the x-axis.

The RSDs increased (Figure 2) as the congeners became more hydrophobic suggesting that equilibrium had not been attained on all samplers during deployment. Referencing a congener from each chlorination level, specifically, CB28, CB52, CB101, CB138, CB180, and CB206, the corresponding RSDs were: 20%, 15%, 34%, 46%, 50%, and 53%, respectively, suggesting that CB28 and CB52 had reached equilibrium based on the previously defined 20% RSD standard. Both the NLS and DIF methods suggested that CB8 and CB28 had a f_eq of 0.9 or greater for most of the PE deployed, CB52 predicted f_eq ≥ 0.9 in half of the PE deployed.

Estimating C_free using the FO method required set stipulations due to instances where the f_ret was greater than one resulting in a negative k_e. In these cases, a k_e correlating to a f_ret of 0.99 was used. The 80/20 rule was not used because these correction restrictions were not applied for the other methods. A minimum f_eq of 0.01 equivalent was used while no upper bound for f_eq was implemented. Applying the FO method decreased C_free RSD values for several of the congeners measured through the pentachlorinated homolog (Figures 2, S4 and S5). Of these, less than a quarter of the congeners had RSDs greater than 20% at NBH2. Hexachlorinated congeners had RSD values greater than 100%. These large RSDs were due to the 76 ¼m measurements. PRC, ¹³C-PCB138, had a measured f_ret greater than one, so a f_eq equivalent of 0.01 was used (NLS and DIF methods predicted f_eqs 0.06), resulting in an estimated C_free that was about five times larger than the other thicknesses measured. This example illustrates the risk of over-correction using the FO method when $C_{PE}^t\text{ and }{C}_{PE}^0$ do not show a significant difference.

The NLS method allowed for an individual f_eq value to be estimated for each target PCB. C_free values calculated using this model resulted in a decrease in measured RSDs throughout the suite of PCBs investigated (Figures 2, S4, S5), relative to other models or no correction at all. Only congener CB126 had a RSD value above 20%. Calculated RSD values ranged from 10 to 23% with a mean of 15% for the suite of PCBs. The 76.2 ¼m PE generally demonstrated the highest C_free estimates followed by the 25.4 ¼m sampler. The C_frees for the 12.7 ¼m and 50.8 ¼m samplers often agreed within one standard deviation of each other (Tables S3a,b).

WBL measurements for the passive samplers ranged from 66 to 268 ¼m (Table S7) and were in agreement with those reported or estimated (Fernandez et al., 2012, Lohmann, 2012, Apell et al., 2016). Only f_ret values between 0.15 and 0.85 were used in the calculation of the WBL for each sampler. Using fraction retained values where an equilibrium may have been achieved (e.g., f_ret < 0.15) resulted in very large WBL thickness estimates. Anomalous WBL values were also observed (both large and very small ranging from 0.6 ¼m to 660 ¼m) when f_ret values were larger than 0.85. Due to analytical uncertainties associated with these endmember f_rets, they were not used, which reduced the estimated WBL RSD by about 30% and, at least, two values were used for each WBL estimation. The triplicate f_eq variability is most notable with the 25.4 ¼m polymer thicknesses measurements. Closer inspection of this dataset from NBH2 revealed the f_ret for ¹³CPCB 28 was acceptable for only two of the replicates. The average WBL for the two replicates that used ¹³C-PCB 28 data are nearly identical and almost double that of the ¹³C-PCB 28 replicate that was not included (f_ret = 0.11). However, the C_free results from the replicate that did not use ¹³CPCB 28 data were closer to the results generated from the other thicknesses. This range in WBL values likely contributed to f_eq variability and ultimately increased C_free RSDs for this method.

Variations observed in the DIF-estimated f_eq resulted in larger C_free RSDs for the four thicknesses tested (Figures 2, S4, S5) than the NLS method. An RSD of greater than 20% was observed for many congeners with a log K_OW ≥ 6.2, though the RSDs did decrease compared to the non-corrected RSD values. Only two congeners, CB126 (35%) and CB189 (30%) had RSDs above 30%, whereas the majority of C_free measurements demonstrated relatively favorable agreement it was not as good as measurements where equilibrium had been attained and over 70% of the PCBs measured had a RSD of 27% or less. Similar to the NLS method, the 25.4 and 76.2¼m PE thicknesses estimated the highest C_free concentrations and in the majority of cases were not significantly different. (Tables S3a and b).

When statistically comparing the C_free by thickness, congeners CB8, CB18 and CB28 demonstrated no significant differences between thicknesses for any of the equilibrium correction methods (Table S9). The occurrence of significantly different C_free estimates between the thicknesses increased starting with the tetrachlorinated PCBs and continued for higher chlorinated congeners. C_free values determined for each thickness using the DIF method were not statistically different 70% of the time. These results may be due, in part, to the relatively large standard deviations between replicates for each thickness resulting in the different thicknesses being difficult to distinguish statistically. Results of similar statistical analyses for NBH4 and NBH5 are provided in Tables S11 and S13. Overall, this data suggests in the cases of the DIF and NLS method using multiple PRCs to deduce WBL or R_S, resulted in similar C_free results between data sets and reduced variation in the results.

Inter-method comparison of congener C_free

Estimates of C_free were also compared by the three equilibrium correction methods used to generate them. Methods were compared by plotting the C_free ratios of the different combinations of correction methods with the target compound’s K_PW (Figure 3). Plotting the data this way illustrates how well the different equilibrium methods agree for compounds as correction factors increased (1/f_eq increased with log K_PW) . C_free values below the quantitation limits were not included, and the data was separated by sampler thickness. Naturally, compounds that reached or nearly reached equilibrium (e.g., CB8, CB18, CB28, CB 44, and CB52) during the deployment showed near perfect agreement for all equilibrium models as little to no corrections were made.

Figure 3.

Inter-method variability of PRC-equilibrium model estimates of C_free, comparing three methods: diffusion based (DIF), sampling rate fit to a nonlinear least square relationship (NLS), and first order kinetic fit (FO) as a function of the polymer partitioning coefficient (K_PW).

The DIF and NLS methods showed the greatest and most consistent agreement of the three approaches tested (Figure 3a). In fact, the C_free values calculated agree within a factor of two for all estimated C_free. On average, the C_free as estimated by the DIF method were 1.1 times larger than those estimated by NLS. The largest differences in C_free were those estimated on the 25.4 ¼m thickness where, on average, the C_free ratio between the two methods was 1.25. C_free ratios ranged from 0.93 to 1.19 for the other thicknesses. This 25.4 ¼m thickness discrepancy is likely due to the unexpectedly high and variable f_ret for PRC ¹³C-PCB28 in this sampler, which resulted in variable and relatively high C_free estimates of the targeted congeners, as discussed in the Intra-Method Comparison of Congener C_free section.

The consistent agreement between these two methods resulted in similar comparisons with the FO method (Figures 3b and c). Overall, the FO-predicted C_free values were, on average, higher than the other two methods. In these comparisons variation increased as the K_PW increased, and as the f_eq decreased, and correction factor increased. Differences larger than a factor of 2, began with PCBs with a log K_PW greater than six. These values correlate to estimated f_eq as high as 0.5. Unlike the DIF and NLS comparison, there was no one thickness of PE that illustrated any observable patterns in variance in the FO comparisons. There were however some observable patterns. These varying behaviors are likely due to some congeners having different physicochemical characteristics than the PRC used to predict their k_e in the FO method. This trend is most observable for all PE thicknesses with log K_PW between 6.80 and 8.25. In both @AB CD⁄ and 364 3EC CD⁄ the C_free ratios are different by a factor of about ten. As K_PW increases to about 7.5 (CB180 has K_PW of 7.42 L/kg) the ratio approaches one. As K_PW exceeds 7.5, the ratios continue to increase indicating the NLS and DIF methods are estimating a larger C_free than the FO method. Much of the variation in these results is a direct result of the large f_ret of the PRC, both ¹³C-CB138 and ¹³C-CB180, had a different default f_ret been defined the patterns may have been different. Many of the large and small ratios observed here incorporated the default f_eq of 0.01 used in the FO model. This result gives further evidence of the risks associated with using the FO model beyond the 80:20 rule in that it can both over- and under-predict C_free estimates.

ANOVA analysis showed that the estimates of C_free demonstrated no statistical differences between results by correction method and C_free estimates when no model was used (Equation 1) for all thicknesses for di- and tri-chlorinated congeners (Table S10). At NBH2, the NLS and DIF C_free estimates were indistinguishable, in 96% of the comparisons tested, and results from the FO method were not statistically different from the NLS and DIF methods in 40% and 34% of the measurements, respectively. Results of similar statistical analyses for NBH4 and NBH5 are reported in Tables S12 and S14, respectively.

Comparison of total PCB C_free

Table 1 reports total PCB C_free values calculated using each of the methods as the sum of up to 27 individual congener C_frees by thickness at NBH2, NBH4 and NBH5. For NBH2, mean C_frees ranged across models and thicknesses with values of 387 to 505 ng/L. For each thickness, the largest total PCB values were generated by the FO method followed by the DIF method, and then the NLS method, where the NLS and DIF methods were always within 5% of each other, and no one thickness of PE consistently demonstrated the largest nor the smallest mean total PCB measurement. No significant differences in total PCB C_free values between methods were determined at NBH2 (Table 1). The same trends were observed at NBH4 although the total PCB C_free range was an order of magnitude lower: 32.2 to 55.6 ng/L. At NBH5, the total PCB C_free were two orders of magnitude below the NBH4 levels with a range of 0.13 to 0.27 ng/L. At NBH4 and NBH5, statistical analyses of total PCB C_frees by thickness detected several significant differences in total PCB C_free estimates (Table 1). However, at all three stations, statistically significant differences between C_frees based on the NLS and DIF methods were never detected. In about 55% of the total PCB C_free estimates a significant difference existed between the FO and NLS or DIF modeled results. These results also illustrate how some congeners can statistically dominate the total PCB estimates. For instance, at NBH2 several of the lighter, faster equilibrating congeners contribute to a large fraction of the total PCB, and as a result, the PRC-modeled results are agreeable with the results to which no PRC corrections were made. However, when these congeners make up a smaller percentage of the mixture significant differences in the results occur. These statistically different results again highlight the importance of using PRCs to estimate accurate C_free. A similar statistical analysis as discussed above but focusing on differences between passive sampler thicknesses by model is reported in Table S15.

Table 1.

Mean total PCB C_free values (ng/L) estimated as the sum of up to 27 individual PCB congeners using each of the correction methods by thickness at NBH2, NBH4 and NBH5

Station	Thickness (¼m)		Model			ANOVA p-value
		No Model	FO	NLS	DIF
NBH2	12.5	385 ± 67.6	396 ± 65.4	395 ± 68.1	396 ± 68.1	0.9963
	25.4	427 ± 65.0	505 ± 91.0	444 ± 68.0	463 ± 83.9	0.6533
	50.8	397 ± 56.2	390 ± 58.4	408 ± 61.2	388 ± 58.5	0.9735
	76.2	305 ± 23.5	456 ± 50.2	387 ± 40.3	401 ± 39.4	0.0772
NBH4	12.5	36.0 ± 0.83B	40.4 ± 2.01A	38.1 ± 1.28A,B	38.9 ± 0.87A	0.0215
	25.4	39.9 ± 1.05C	55.6 ± 1.75A	43.7 ± 1.01B,C	47.8 ± 4.45B	0.0003
	50.8	27.1 ± 1.60C	43.8 ± 1.10A	32.2 ± 1.26B	34.3 ± 1.16B	<0.0001
	76.2	26.8 ± 1.46C	47.1 ± 1.26A	39.7 ± 1.13B	39.3 ± 0.64B	<0.0001
NBH5	12.5	0.18 ± 0.01C	0.25 ± 0.01B	0.26 ± 0.01A,B	0.27 ± 0.02A	<0.0001
	25.4	0.09 ± 0.03A	0.13 ± 0.04A	0.17 ± 0.06A	0.18 ± 0.06A	0.1853
	50.8	0.07 ± 0.01B	0.13 ± 0.01A	0.14 ± 0.01A	0.14 ± 0.01A	<0.0001
	76.2	0.06 ± 0.01C	0.13 ± 0.01B	0.16 ± 0.01A	0.17 ± 0.01A	<0.0001

This comparison of mass transfer-based correction methods for passive samplers found that using multiple PRCs to estimate sampling rates or fractional equilibria for target PCBs (i.e., NLS and DIF methods, respectively) resulted in more consistent and precise estimates of C_free than using results from one PRC (i.e., the FO method). In addition, the NLS and DIF methods generated C_free values that were statistically similar when expressed as total PCB or on a single congener basis. These findings suggest that contaminated site managers and scientists can apply either mass transfer method to use PRC results to estimate C_free for their target contaminants. Assistance running DIF method is available on-line (https://www.serdp-estcp.org/Tools-andTraining/Tools/PRC-Correction-Calculator and https://www.epa.gov/superfund/superfundcontaminated-sediments-guidance-documents-fact-sheets-and-policies). Assuming equilibrium is discouraged as it will likely under-estimate C_free for contaminants that are slow to equilibrate or under in situ conditions with slow kinetics (i.e., quiescent environmental conditions). For all methods, it is important to consider using PRCs that span the physicochemical characteristics (e.g., log K_OW) of the target HOCs and that will result in useful f_ret, guidance on estimating PRC results given environmental conditions can be found in the literature (Apell et al., 2016).