Article pubs.acs.org/est
Modeling Uptake of Hydrophobic Organic Contaminants into Polyethylene Passive Samplers Jay M. Thompson, Ching-Hong Hsieh, and Richard G. Luthy* Department of Civil and Environmental Engineering, Stanford University, Stanford, California 94305-5080, United States S Supporting Information *
ABSTRACT: Single-phase passive samplers are gaining acceptance as a method to measure hydrophobic organic contaminant (HOC) concentration in water. Although the relationship between the HOC concentration in water and passive sampler is linear at equilibrium, mass transfer models are needed for nonequilibrium conditions. We report measurements of organochlorine pesticide diffusion and partition coefficients with respect to polyethylene (PE), and present a Fickian approach to modeling HOC uptake by PE in aqueous systems. The model is an analytic solution to Fick’s second law applied through an aqueous diffusive boundary layer and a polyethylene layer. Comparisons of the model with existing methods indicate agreement at appropriate boundary conditions. Laboratory release experiments on the organochlorine pesticides DDT, DDE, DDD, and chlordane in well-mixed slurries support the model’s applicability to aqueous systems. In general, the advantage of the model is its application in the cases of well-agitated systems, low values of polyethylene−water partioning coefficients, thick polyethylene relative to the boundary layer thickness, and/or short exposure times. Another significant advantage is the ability to estimate, or at least bound, the needed exposure time to reach a desired CPE without empirical model inputs. A further finding of this work is that polyethylene diffusivity does not vary by transport direction through the sampler thickness.
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INTRODUCTION Measuring the concentration of hydrophobic organic compounds (HOCs, e.g., DDT, PCBs, PAHs) in water via direct extraction is often laborious and expensive.1 Single-phase, polymeric passive samplers are increasingly used for measuring HOC concentrations in water,2−4 air,5,6 and sediment pore water.7−14 The most widely used polymers for passive samplers include polyoxymethylene (POM), polydimethylsiloxane (PDMS) and polyethylene (PE). This work focuses on PE due to its robustness and ubiquity, but the approach is general and can be applied to any polymer if the transport processes are similar, e.g., Fickian diffusion through the polymer and polymer properties are constant across the sampler thickness (see the Supporting Information, Figure S6). At equilibrium, the relationship between HOC concentration in the water and polyethylene phase is linear: CW =
C PE KPE
Although linear partitioning relationships can relate aqueous and PE concentrations at equilibrium, these conditions rarely exist in typical sediment conditions where transport to the PE is limited by slow mass transfer. Even HOCs in surface waters may not reach equilibrium with PE within practical exposure times. For instance, Lohmann estimates that aqueous benzo[a]pyrene reaches only 50% of equilibrium PE concentration after 1 year deployment time in quiescent water.15 To convert nonequilibrium PE concentrations to water concentrations, a performance reference compound (PRC) can be used.16 PRCs are impregnated into the PE material prior to deployment. By measuring the amount of PRC released from the PE to the sediment or water, the rate of mass transfer can be estimated with a mathematical model. The most widely used mass transfer model relating PRC release to target compound uptake is an exponential model that assumes linear concentration profiles in an aqueous boundary layer phase and, in some cases, the polyethylene phase. Because the actual concentration profile is a Fickian concentration front, the exponential model may be inappropriate for modeling PE concentrations under conditions in which polyethylene-phase resistance is significant, e.g., towing PE from a boat or anchored
(1)
where CPE (MHOC VPE−1) and CW (MHOC VW−1) are both in units of mass/volume and KPE is the unitless (VW VPE−1) polyethylene−water partition coefficient.15 As KPE for HOCs is typically 104−107, less than 1 g of PE is needed to detect environmentally relevant HOC concentrations. Note that KPE may also be presented in units of VW MPE−1. Unless otherwise noted, KPE will refer to the unitless (VW VPE−1) polyethylene− water partition coefficient. © XXXX American Chemical Society
Received: September 10, 2014 Revised: January 18, 2015 Accepted: January 21, 2015
A
DOI: 10.1021/es504442s Environ. Sci. Technol. XXXX, XXX, XXX−XXX
Article
Environmental Science & Technology
filled with water, approximately 0.1 g of PE, and 1 g of sodium azide. The jars were agitated for 5 weeks at 100 rpm. After the contact period, the PE strip and a water sample were separately withdrawn and analyzed. Polyethylene diffusion coefficients were determined by the film stacking method.19 A PE strip (7 × 2 cm) impregnated with pesticides was stacked on top of four unimpregnated PE strips of identical size. The stack was sandwiched between two glass microscope slides and weight was applied resulting in an approximate pressure of 10 kPa. Trials were performed in triplicate. After 12, 24, and 48 h, stacks were disassembled and the PE strips were analyzed for pesticides. The diffusion of pesticides from the impregnated strip to the clean strips is a function of time, strip thickness, the number of strips and DPE. Note that, unlike slurry methods, film stacking does not introduce the potential confounding factor of an aqueous boundary layer mass transfer resistance. The distribution of pesticides in each strip is described as given by Crank17
in a fast-moving river. A single-phase Fickian model exists that does not make the linearity assumption.17 However, this model entirely neglects aqueous boundary layer resistance. This is a significant drawback in natural systems in which aqueous resistance is likely. Therefore, a model that considers Fickian diffusion in both the aqueous and PE phase is more general than either of the aforementioned models. Such a model is especially beneficial for describing transfer at short times, with thick PE, under vigorous mixing, and/or with less hydrophobic compounds. Although a numeric solution to this model has been described in the literature,4 no analytical solution has been described in the passive sampling literature. This work develops such an analytical solution and then validates it, first mathematically then experimentally. Although this work focuses on polyethylene passive samplers, the two-phase Fickian modeling can be easily adapted to any passive sampler undergoing one-dimensional mass transfer. This work has three objectives. One, to apply a mathematical model describing the uptake and release of compounds to and from PE as two coupled diffusion processes, one in the PE phase and another in an aqueous boundary layer phase. Two, to test the validity of the model against boundary cases and a controlled laboratory study. Three, to determine the utility of the model against existing models and determine when the additional mathematical approach is necessary. Meeting the second objective required determining the KPE and diffusivity in polyethylene for organochlorine pesticides, many of which have not yet been determined.
⎧h 2 C = C0⎨ + ⎪ π ⎩l ⎪
cos
∞
∑ 1 sin nπh exp(−DPEn2π 2t /l 2) n=1
n
l
nπx ⎫ ⎬ l ⎪ ⎭ ⎪
(2)
where h is the thickness of the impregnated PE strip, l is the overall thickness of the stack, n is the index of summation, and x is measured from the edge of the preloaded strip that is adjacent to the glass. Experimental data were fit to Crank’s model and DPE was determined by nonlinear regression. PE Diffusion Slurry Studies. PE strips, preloaded with pesticides and of approximate mass 0.05 g, were placed in 40 mL amber glass vials filled with deionized water and 1 g of powdered activated carbon. Activated carbon was added keep the bulk water concentration as close to zero as possible. Each vial was agitated at 100 rpm for predetermined time periods, after which the vial was sacrificed and the PE analyzed for pesticides. Model Derivation. A model based on two Fickian diffusion processes was used to describe the PE/water system. Diffusion was assumed to occur through two phases: PE and an aqueous diffusive boundary layer (DBL). A mathematical approach similar to the one by Fernandez et al.8 (and later developed into a software package14) was employed with the boundary conditions changed to reflect a finite aqueous boundary layer rather than an infinite sediment phase. For a PE sampler with half-thickness of l and a diffusive boundary layer thickness of δ, the diffusion of HOC can be described as
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MATERIALS AND METHODS Materials. Low-density polyethylene (PE, 51 μm thick, 0.92 g cm−3 density) was obtained from Brentwood Plastics (St. Louis, MO). Pesticide grade solvents were purchased from Fischer Scientific (Fair Lawn, NJ). Eleven pesticide were examined in this study, cis- and trans-chlordane, transnonachlor, 2,4′- and 4,4′-DDT, DDE, and DDD (dichlorodiphenyltrichloroethane, dichlorodiphenyldichloroethylene, and dichlorodiphenyldichloroethane, respectively), 4,4′DDMU (dichlorodiphenylmonochloroethylene), and dieldrin. Pesticide standards were obtained from Ultra Scientific (N. Kingstown, RI). Activated carbon (Type-TOG, Calgon Carbon, Pittsburgh, PA) was pulverized to a powder using a stone mill. PE was cleaned with hexane, acetone, and deionized water for 12 h each as described elsewhere.13 When needed, PE was preloaded with pesticides as described by Booij et al.18 An 80:20 methanol/water solution was spiked with pesticides and contacted with PE. The solution was mixed at 100 rpm for 3 days. Immediately after withdrawal, the strips were thoroughly wiped with a lint-free tissue to prevent uneven compound surface loading due to evaporation. Preloaded strips were stored in amber glass bottles at 4 °C for a maximum of 2 weeks prior to use. Modeling indicated that all of the studied compounds would be evenly distributed after 24 h (see Supporting Information, Figure S1). Extraction, cleanup, and analysis of PE samplers are described in the Supporting Information. KPE and PE Diffusivity (DPE) Determination. KPE was determined by exposing PE strips to aqueous organochlorine pesticide solutions with concentrations varying between 1 and 1000 ng/L. A pesticide solution in hexane was spiked into a 1 L amber glass jar. A gentle stream of nitrogen gas was directed into the jar until the hexane evaporated. The jars were then
∂C PE ∂ 2C PE = DPE ∂t ∂x 2 ∂C DBL ∂ 2C DBL = DW ∂t ∂x 2
for 0 < x < l
for l < x < l + δ
(3)
(4)
where the center of the strip is positioned at x = 0, DPE and DW are the diffusivities (m2/s), and CPE and CDBL are the concentrations in polyethylene and water (ng/m3), respectively. Diffusion is assumed to be a one-dimensional process through the strip thickness. The following boundary conditions apply: B
DOI: 10.1021/es504442s Environ. Sci. Technol. XXXX, XXX, XXX−XXX
Article
Environmental Science & Technology
Table 1. Summary of Measured KPE and DPE Valuesa
local equilibrium at the PE−water interface: C PE = KPEC DBL
at x = l
(5)
compound
where KPE is unitless (VW VPE−1).
trans-chlordane cis-chlordane trans-nonachlor dieldrin 4,4′-DDMU 2,4′-DDE 4,4′-DDE 2,4′-DDD 4,4′-DDD 2,4′-DDT 4,4′-DDT
no flux across the midline of the strip due to symmetry: dC PE =0 dx
at x = 0
(6)
equal fluxes across the PE−water interface due to conservation of mass: DPE
dC PE dC = D W DBL dx dx
at x = l
(7)
at x = l + δ
(8)
−13.51 −13.51 −13.56 −13.58 −13.06 −13.19 −13.32 −13.34 −13.41 −13.47 −13.58
(±0.04) (±0.02) (±0.03) (±0.09) (±0.13) (±0.04) (±0.07) (±0.05) (±0.06) (±0.04) (±0.05)
approximately 1.5 log units, from 4.36 for dieldrin to 5.88 for 4,4′-DDE. KPE values for DDTs were similar to those found by Hale et al., with the average difference between this study and Hale et al. being 0.1 log units.20 KPE for dieldrin varied by 0.3 log units from literature values.21 While, there are no literature values for chlordane and nonachlor, Lohmann15 provides a correlation between compound solubility and KPE for organochlorine pesticides of
(9)
log KPE = − 1.07log C W,sat + 2.16
where M̂ is M/M∞ in the Laplace domain, δ̂ is the nondimensionalized DBL thickness δ/l, ψ is the ratio of diffusivities DW/DPE, and s is the Laplace parameter based on nondimensional time (T = (tDPE)/l2). Release of PRCs an be expressed as −1 ⎧ ⎛ ⎞⎫ δ̂ s K tanh ⎪ ⎜ PE ⎟⎪ ψ 1 + coth s ⎟⎬ M̂ = − ⎨s 3/2⎜ s ψ ⎟⎪ ⎪ ⎜ ⎠⎭ ⎩ ⎝
(±0.03) (±0.03) (±0.04) (±0.17) (±0.13) (±0.07) (±0.09) (±0.03) (±0.04) (±0.05) (±0.05)
Values in parentheses represent the standard deviation of KPE observations (n = 6) or the 95% confidence interval on estimates of DPE based on nonlinear regression of PE stacking experimental data. Note that KPE is presented in the traditional units of LW kgPE−1 here, not VW VPE−1 as in the model description.
The initial condition is CDBL = CW and CPE = 0 for all values of x at t = 0. By solving this system of partial differential equations for the concentration profiles CDBL and CPE for the given boundary and initial conditions and integrating CPE over the thickness of the sampler, the following expression for relative mass uptake can be found: −1 ⎧ ⎛ ⎞⎫ δ̂ s ⎪ 3/2⎜ KPE tanh ψ ⎟⎪ + coth s ⎟⎬ M̂ = ⎨s ⎜ ψ ⎟⎪ ⎪ ⎜ ⎠⎭ ⎩ ⎝
5.17 5.15 5.54 4.36 5.44 5.83 5.88 4.77 4.84 5.86 5.60
log DPE (m2/s)
a
boundary layer concentration is equal to the bulk water concentration at the DBL−bulk water interface: C DBL = C W
log KPE (LW kgPE−1)
(11)
Solubility data for the studied pesticides were obtained from Schenker et al.22 The determined KPE for trans- and cischlordane agreed quite well with this relationship with differences of 0.08 and 0.03 log units, respectively. There are insufficient solubility data published on trans-nonachlor to make this correlation. However, it is likely that trans-nonachlor is less soluble than chlordane, due to its higher octanol−water partition coefficient, KOW, of approximately 0.7−0.8 log units, as estimated by SPARC. Therefore, the observation of the higher KPE for trans-nonachlor compared to the one for chlordane is consistent with its chemical properties. PE diffusivity was determined by nonlinear regression of PE stacking data. Example stacking data are shown in Figure 1. In most cases, the data fit the model, as described by eq 2, quite well, with the 95% DPE confidence interval (on the regression coefficient estimate of DPE) being ±
