Letter pubs.acs.org/journal/estlcu
Kinetics and Pathway of Vinyl Fluoride Reduction over Rhodium Yu-Han Yu†,‡ and Pei C. Chiu*,† †
Department of Civil and Environmental Engineering, University of Delaware, Newark, Delaware 19716, United States Department of Environmental Engineering, National Chung-Hsing University, Taichung 40227, Taiwan
‡
S Supporting Information *
ABSTRACT: Fluorinated compounds have become prevalent in ecosystems because of their widespread use, yet few methods that can effectively degrade these pollutants exist. We investigated the catalytic reduction of vinyl fluoride (VF), a regulated high-volume chemical and probable carcinogen, over rhodium in H2 gas or aqueous solution. Water controlled both the kinetics and products of VF reduction. In dry H2 gas, VF was reduced through primarily hydrogenation, at rates that were too fast to measure. In liquid water, reaction was firstorder in both VF and rhodium concentrations and proceeded predominantly through hydrodefluorination. Experiments and calculations show the reaction was mass transfer-limited. Even adsorbed water molecules on the catalyst surface posed a significant mass transfer barrier and dramatically altered product selectivity. These results provide insights into the kinetics and pathway of VF defluorination and are important for the design of studies that aim to elucidate the reduction mechanisms of and develop treatment methods for fluorocarbons.
■
INTRODUCTION Fluorinated hydrocarbons have been increasingly used as surfactants, refrigerants, stain-resistant agents, and fluoroplastic monomers in recent decades.1,2 As a result, these chemicals are ubiquitous in the environment.3−6 Fluorinated compounds are generally more inert than their chlorinated counterparts because of the greater stability of carbon−fluorine bonds.7,8 Many fluorocarbons are also toxic, bioaccumulative, carcinogenic, and persistent,7,9 and hence, their prevalence has raised growing ecological and human health concerns.7,10 Over the past half-century, significant resources were invested to combat chlorinated compounds, from pesticides and biphenyls to solvents and disinfection byproducts, and many chemical and biological agents were discovered and/or developed to deal with these pollutants. In contrast, few agents that can effectively degrade fluorocarbons exist. No microorganism has been found that can reductively defluorinate,11,12 whereas chemical defluorination often requires a high temperature, a high pressure, and/or nonaqueous solvents.13,14 However, recent work by Baumgartner and McNeill14,15 demonstrates that rhodium can catalyze the reductive defluorination of fluorinated benzenes by H2 under ambient (room temperature and 1 atm) conditions, suggesting it might be feasible to develop a rhodium-based catalyst to degrade fluorocarbons. These authors showed that all fluorinated benzenes were rapidly reduced in water and that hydrodefluorination was the preferred reaction over hydrogenation. In this study, we investigated the reductive transformation of fluorinated alkenes over rhodium in both aqueous and gas phases, using vinyl fluoride (VF) as a model compound. VF is a © XXXX American Chemical Society
high production volume (HPV) chemical used primarily for the production of polyvinyl fluoride and other fluoro polymers, which have been increasingly applied to the surfaces of pipes, buildings, and aircraft cabins.16,17 As other vinyl halides, VF is regulated by the U.S. Environmental Protection Agency under the Toxic Substance Control Act (TSCA) and was recently added to the Toxic Release Inventory (TRI).18 VF is metabolized in a manner similar to that of vinyl chloride18 and is classified as a probable (IARC Group 2A) carcinogen.19 Here, we determined the rate law, identified the rate-limiting step, and elucidated the critical role water played in controlling both the kinetics and the pathway of VF reduction over rhodium.
■
MATERIALS AND METHODS Hydrogen (99.999%) was purchased from Keen Compressed Gas (Wilmington, DE). Ethane and ethene were obtained from Scotty Gas (Houston, TX). Fluoroethane (C2H5F, 99%) and VF (C2H3F, 98%) were acquired from SynQuest Laboratories (Alachua, FL). Deionized water (>18 MΩ) was used to prepare all solutions. Rhodium on γ-alumina [Rh/Al2O3, 5% (w/w) Rh] was obtained from Sigma-Aldrich (St. Louis, MO) and stored in a desiccator with drierite before being used. The specific surface area of Rh/Al2O3, measured by N2 adsorption using a Received: September 22, 2014 Revised: October 18, 2014 Accepted: October 20, 2014
A
dx.doi.org/10.1021/ez500291g | Environ. Sci. Technol. Lett. XXXX, XXX, XXX−XXX
Environmental Science & Technology Letters
Letter
NOVA Surface Area Analyzer 2000 (Quantachrome, Boynton Beach, FL), was 153.2 ± 3.0 m2 g−1. Aqueous-phase experiments were performed in 250 mL amber glass bottles (Fisher, Pittsburgh, PA) containing 50 mL of 10 mM Tris buffer solution (pH 8.2) and a predetermined amount of catalyst. Each bottle was purged with H2 for 1.5 h before it was sealed with a Mininert valve (Vici, Houston, TX) and vinyl tape (3M, St. Paul, MN). Blank (without catalyst) and control (with N2) bottles were set up in parallel. Reaction was initiated by introducing a known quantity of VF into the reactor headspace. The setup for the gas-phase experiments was similar except that the Tris solution was omitted; i.e., each bottle was purged (1.5 h) and filled with moisture-free H2 at 1 atm. Multiple doses of VF (∼10.4 μmol each) were injected for each gas-phase experiment. Additional gas-phase experiments were conducted with humidified H2, prepared by passing H2 through a humidifier consisting of an air stone and varied amounts of deionized water to produce relative humidities (RHs) of 53.0 ± 0.1, 67.5 ± 0.1, 80.5 ± 0.1, and 100% for calibration and 96 ± 0.1% for experiments. The reactor temperature was fixed at 22 ± 0.05 °C using a double jacket with a water bath to prevent humidity from fluctuating during reaction. An Agilent (Santa Clara, CA) 6890 gas chromatograph equipped with a flame ionization detector and a GSGasPro column (0.32 mm × 30 m, Agilent) was used to measure VF and its reduction products. Ethane, ethene, fluoroethane, and VF were quantified on the basis of fivepoint calibration curves. The water vapor concentration in the reactor headspace was determined using an Agilent 6890N gas chromatograph with a DB-5 ms column and a 5973N mass spectrometer with selective ion monitoring (m/z 18).
Figure 1. (a) Concentration profiles of VF and its products during reduction of 20.8 μmol of VF in 250 mL reactors containing 50 mL of a 10 mM Tris solution and 0.86 mg of Rh/Al2O3 catalyst [5% (w/w) Rh]. The fitted curves are based on the pathway in Figure 2 and the assumption that all the reactions are pseudo-first-order. Error bars represent standard deviations. (b) Cumulative masses of fluoroethane and ethane formed over five 10.4 μmol doses of VF added sequentially to gas-phase reactors, each containing pure H2 and 0.86 mg of Rh/ Al2O3 catalyst [5% (w/w) Rh].
■
RESULTS AND DISCUSSION Liquid-Phase Experiments. In the presence of water, VF was reduced exponentially to ethane as a main product (Figure 1a), with a fitted pseudo-first-order rate constant (k1′) of 7.96 × 10−5 s−1. Low concentrations of ethene and fluoroethane were also observed, apparently as an intermediate and an end product, respectively. To confirm these, we performed separate experiments using ethene or fluoroethane as a starting material under identical conditions. We observed quantitative reduction of ethene to ethane but no transformation of fluoroethane over a month. This indicates that ethane was formed through ethene rather than fluoroethane as an intermediate, that VF was reduced via both hydrodefluorination (to ethene) and hydrogenation (to fluoroethane), and that hydrodefluorination was the preferred reaction. On the basis of these results, a VF reduction pathway is proposed (Figure 2), which involves two parallel routes: hydrodefluorination followed by hydrogenation (to ethane), and hydrogenation. The predominant route is analogous to the reaction sequence proposed by Baumgartner and McNeill,14 suggesting that, in water, fluorinated benzenes and alkenes probably react in a similar manner over Rh. Under the reaction conditions, each Rh atom catalyzed ∼100 reduction reactions (of VF and ethene) on average, and the mole ratio (R) of the end products, fluoroethane and ethane, was 0.022. Assuming all reactions in Figure 2 are first-order, we obtained a good fit to the data (R2 > 0.99) for VF and ethane (Figure 1a). When experiments were repeated under identical conditions using different amounts of catalyst, the pseudo-firstorder rate constant k1′ was found to be proportional to the Rh concentration (Figure S1 of the Supporting Information). Hence, the rate law for VF reduction in water is second-order,
Figure 2. Proposed VF reduction pathway based on products observed in aqueous- and gas-phase reactions in Figure 1.
as shown in eq 1. The second-order rate constant (k2) obtained through linear regression was 9.36 s−1 (mol of Rh)−1 L−1 (R2 = 0.9995). −
d[VF] = k1′[VF]1 = k 2[VF]1 [Rh]1 dt
(1)
Gas-Phase Experiments. For VF reduction in H2 gas, we were unable to obtain concentration profiles similar to those depicted in Figure 1a, because all VF reacted by the time the first sample was taken. As in the reaction in water, VF was transformed to both ethane and fluoroethane, which combined accounted for all the added VF mass. However, fluoroethane, rather than ethane, was the main product in the gas-phase B
dx.doi.org/10.1021/ez500291g | Environ. Sci. Technol. Lett. XXXX, XXX, XXX−XXX
Environmental Science & Technology Letters
Letter
reactors. Additional aliquots (∼10.4 μmol each) of VF were spiked repeatedly, but VF was never observed; thus, its reaction rate in H2 could not be determined. Figure 1b shows the cumulative masses of ethane and fluoroethane formed. The fluoroethane-to-ethane mole ratio (R) was constant at 36.5 over five doses of VF (>130 turnovers). Hence, in sharp contrast to its reaction in water, VF was reduced predominantly via hydrogenation in dry H2 gas, at rates that were too fast to measure using our experimental setup. The striking differences in both the kinetics and the pathway between the liquid- and gas-phase systems suggest that water played a critical role in controlling VF reduction over Rh/Al2O3. Rate-Limiting Step. Because we monitored only gas-phase concentrations, for VF reduction to be observed in liquid-phase experiments, VF must be (1) transported from the headspace into water, (2) transferred from bulk water to the catalyst surface, and (3) adsorbed to the catalyst before reduction.20,21 Because steps 1 and 2 were absent in the gas-phase experiments, the rapid reduction of VF means that adsorption and reduction of VF were intrinsically fast, and that the ratelimiting step in the liquid-phase experiments was most likely a mass transfer process (i.e., step 1 or 2). Moreover, because the pseudo-first-order rate constant k1′ was proportional to Rh content (Figure S1 of the Supporting Information), step 1 can be ruled out, because k1′ would be independent of Rh content if the gas-to-liquid mass transfer were limiting. This leaves step 2 as the remaining candidate. To assess whether step 2 was the rate-limiting step, we calculated the liquid-to-particle mass transfer constant kMT, using the method described by Arnold et al.,22 and an empirical relationship among Sherwood number (Sh), Reynolds number (Re), and Schmidt number (Sc):23,24 Sh =
radius of water molecule to be 1.68 Å,27 this corresponds to 20−57 μmol of surface-bound water. Under these conditions, the amount of water vapor in the reactor was 260 μmol and its partial pressure was 2564 Pa, which represents the initial fugacity of both the gaseous and adsorbed water. Results of a prehumidified H2 experiment are shown in Figure 3. As in all the other experiments, the VF mass added
Figure 3. (a) Concentration profiles and mass balance during reduction of five doses of VF (10.4 ± 0.3 μmol/dose) in 250 mL reactors containing prehumidified H2 and 0.86 mg of Rh/Al2O3 catalyst [5% (w/w) Rh]. The temperature of the reactors was maintained at 22 ± 0.05 °C throughout the experiment. (b) Firstorder rate constants of VF reduction, fluoroethane-to-ethane mole ratios, and water vapor concentrations (expressed as relative humidity) during reduction of five (10.4 ± 0.3 μmol) doses of VF. Error bars represent standard deviations. The solid line represents the first-order rate constant for VF reduction in water (i.e., from Figure 1a), and the dashed lines represent one standard deviation.
kL*dP DW
= 2 + 0.6(Re)0.5 (Sc)0.33 ⎛ d u ⎞0.5 = 2 + 0.6⎜ P ⎟ (v /D W )0.33 ⎝ v ⎠
(2)
where kL* is the uncorrected mass transfer coefficient (meters per second), dP is the diameter of Rh/Al2O3 particles (50 μm), DW is the molecular diffusivity of VF in water (1.4 × 10−9 m2/ s), u is the terminal velocity of Rh/Al2O3 particles in water (3.8 × 10−3 m/s), and ν is the kinematic viscosity of water (1.0 × 10−6 m2/s). For the data in Figure 1a, the geometric surface area-to-liquid volume ratio (a) was 0.54 m2/m3, and kL* was calculated to be 1.2 × 10−4 m/s. Using the correction factor of 1.2 proposed by Harriott,24 kMT = 1.2kL*a = 7.8 × 10−5 s−1. This value is practically identical to the observed pseudo-firstorder rate constant (k1′ = 7.96 × 10−5 s−1). Therefore, results of our experiments and calculations support the transport of VF molecules from bulk water to the catalyst surface being the ratelimiting step in liquid-phase reactors. Humidified Gas-Phase Experiments. To investigate the effects of water on the VF reduction kinetics and pathway, we conducted additional gas-phase experiments using H2 with a 96 ± 0.1% RH at a constant temperature of 22 ± 0.05 °C. The humidity of 96% was chosen to ensure a high adsorbed water content and to avoid free water formation (i.e., condensation) due to minute temperature fluctuations. Under these conditions, the Al2O3 (0.86 mg) surface would be covered by 8−23 layers of adsorbed water molecules.25,26 If we take the
(five doses) was fully reduced and recovered as ethane and fluoroethane. Figure 3a shows that even layers of adsorbed water molecules slowed VF reduction sufficiently that the rate constants became measurable. Interestingly, with each additional dose, the first-order rate constant decreased successively (Figure 3b), approaching the k1′ value obtained in the liquidphase experiments. Because we could measure only mass transfer but not adsorption or reduction rate, the decreasing rate constant suggests the mass transfer barrier increased with an increasing mass of VF transformed. Note that no discernible change in rate occurred over the same time and VF dosage in the liquid- and gas-phase reactors, respectively (Figure 1a,b). In addition, the adsorbed water layers significantly shifted the product distribution, changing the R value from 36.5 in dry H2 to between 2 and 6 in humidified H2. With each additional VF dose, R decreased sequentially from 5.1 to 2.5 (Figure 3b). The results in Figure 3 are consistent with those from the liquid- and gas-phase experiments and confirm the pivotal role of water in VF reduction. Even layers of surface-bound water molecules posed a pronounced mass transfer barrier that limited the overall VF reaction rate and altered the reaction C
dx.doi.org/10.1021/ez500291g | Environ. Sci. Technol. Lett. XXXX, XXX, XXX−XXX
Environmental Science & Technology Letters
Letter
route and final product distribution dramatically. We hypothesized that these results, and the decreasing k1′ and R in Figure 3b, were due to the fact that hydrodefluorination produces ions, i.e., H+ and F, whereas hydrogenation does not. These two reactions presumably involved different Rhbound transition states. Because hydration of H+ and hydration of F are highly exothermic (−1090 and −506 kJ/mol,28 respectively), if water were present in the vicinity of Rh, it would stabilize the relatively polar, partially charged transition state for hydrodefluorination and thus favor the formation of ethene, H+, and F. This explains the low, high, and intermediate R values in liquid water, dry H2, and humidified H2, respectively. In the humidified H2 experiments, the formation and hydration of H+ and F would create a local osmotic imbalance at or near Rh, which would drive the migration of surface water from neighboring regions, as well as water vapor from the headspace, toward Rh, leading to an overall lower water fugacity in the reactor. Accumulation of water around Rh due to continued ion formation would create an increasingly thicker water layera growing igloo of salty bound waterover Rh, resulting in the slowing mass transfer rate and increasing hydrodefluorination observed in the humidified H2 experiment. Our hypothesis hence predicts that water fugacity would decrease with an increasing mass of VF transformed. To test this, we measured the concentration of water vapor in the headspace of humidified H2 reactors. As shown in Figure 3b, the water concentration (expressed in % RH) indeed decreased with time, from 96% initially to ∼81% after three additions of VF. The ion source of the detector was contaminated at the time of measurement for the fourth VF dose, and thus, a measurement for the fifth dose was not performed. This change in RH corresponds to a decrease of 400 Pa in water fugacity and removal of 41 μmol of water vapor, equivalent to 0.7−2 times the initial mass of adsorbed water. Given the cumulative mass of HF produced [11.65 μmol (Figure 3a)], the final ionic strength of the surface water would be between 7 and 11 M. The concentrated HF might have reacted with Al2O3 and/or Rh, further contributing to the observed decrease in rate. Energy-dispersive X-ray spectroscopy (EDX) element mapping of fresh and used (dried) catalyst illustrates a uniform distribution of Rh on the surface of the former and of fluorine on the surface of the latter (Figures S2 and S3 of the Supporting Information). It is instructive to compare our VF results and those of Baumgartner and McNeill on halogenated benzenes.14,15 First, in water, hydrodefluorination and hydrogenation of fluorobenzene occurred sequentially. For VF, in contrast, these reactions occurred in parallel in both gas and aqueous phases, albeit at very different ratios. This may reflect the reactivity of the double bond of VF being higher than the reactivities of those of fluorinated benzenes. Second, the finding that VF reduction was controlled by mass transfer through (liquid or bound) water suggests the reduction of fluorinated benzenes in water might also be mass transfer-limited. While rates of reduction of poly halo and nitro congeners typically vary over many orders of magnitude,29 the observed rate constants of 12 mono- to hexafluorinated benzenes ranged only from 0.6 to 3.7 h−1.15 Moreover, these rate constants are within an order of magnitude of the mass transfer rate constants calculated using eq 2 (0.47 ± 0.04 h−1). In addition, while chlorinated and fluorinated benzenes exhibited different regioselectivities,15 their rate constants were practically the same,15 suggesting
that reduction of chlorinated benzenes over Rh in water might be mass transfer-controlled, as well. If this premise is true, kinetics would not be a suitable tool for probing the reduction mechanisms of halogenated benzenes and alkenes because of the mass transfer-limited nature of the reactions. Other methods, such as isotopic techniques,14 may be more useful. Finally, the inability of Rh to reduce fluoroethane suggests the need to seek or develop alternative catalysts that can cleave saturated carbon−fluorine bonds.
■
ASSOCIATED CONTENT
S Supporting Information *
Aqueous-phase rate constants for different Rh contents and scanning electron microscopy/EDX images of fresh and used catalyst. This material is available free of charge via the Internet at http://pubs.acs.org.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail: pei@udel.edu. Phone: (302) 831-3104. Fax: (302) 831-3640. Notes
The authors declare no competing financial interest.
■
REFERENCES
(1) Lewandowski, G.; Meissner, E.; Milchert, E. Special applications of fluorinated organic compounds. J. Hazard. Mater. 2006, 136, 385− 391. (2) Barber, J. L.; Berger, U.; Chaemfa, C.; Huber, S.; Jahnke, A.; Temme, C.; Jones, K. C. Analysis of per- and polyfluorinated alkyl substances in air samples from Northwest Europe. J. Environ. Monit. 2007, 9, 530−541. (3) Senthilkumar, K.; Ohi, E.; Sajwan, K.; Takasuga, T.; Kannan, K. Perfluorinated Compounds in River Water, River Sediment, Market Fish, and Wildlife Samples from Japan. Bull. Environ. Contam. Toxicol. 2007, 79, 427−431. (4) Olsen, G. W.; Burris, J. M.; Ehresman, D. J.; Froehlich, J. W.; Seacat, A. M.; Butenhoff, J. L.; Zobel, L. R. Half-Life of Serum Elimination of Perfluorooctanesulfonate, Perfluorohexanesulfonate, and Perfluorooctanoate in Retired Fluorochemical Production Workers. Environ. Health Perspect. 2007, 115, 1298−1305. (5) Houde, M.; Martin, J. W.; Letcher, R. J.; Solomon, K. R.; Muir, D. C. G. Biological Monitoring of Polyfluoroalkyl Substances: A Review. Environ. Sci. Technol. 2006, 40, 3463−3473. (6) Prevedouros, K.; Cousins, I. T.; Buck, R. C.; Korzeniowski, S. H. Sources, Fate and Transport of Perfluorocarboxylates. Environ. Sci. Technol. 2006, 40, 32−44. (7) Blake, D.; Howell, R. D.; Criddle, C. S. Fluorinated organics in the biosphere. Environ. Sci. Technol. 1997, 31, 2445−2454. (8) Braun, T.; Wehmeier, F. C-F Bond Activation of Highly Fluorinated Molecules at Rhodium: From Model Reactions to Catalysis. Eur. J. Inorg. Chem. 2011, 613−625. (9) Zhang, X.-J.; Lai, T.-B.; Kong, R. Y.-C. Biology of Fluoro-Organic Compounds. In Topics in Current Chemistry; Springer: Berlin, 2011; Vol. 308, pp 365−404. (10) Adams, D. E. C.; Halden, R. U. ACS Symposium Series; Halden, R. U., Ed.; American Chemical Society: Washington, DC, 2010; pp 539−560. (11) Ma, R.; Shih, K. Perfluorochemicals in wastewater treatment plants and sediments in Hong Kong. Environ. Pollut. 2010, 158, 1354− 1362. (12) Boulanger, B.; Vargo, J. D.; Schnoor, J. L.; Hornbuckle, K. C. Evaluation of Perfluorooctane Surfactants in a Wastewater Treatment System and in a Commercial Surface Protection Product. Environ. Sci. Technol. 2005, 39, 5524−5530. D
dx.doi.org/10.1021/ez500291g | Environ. Sci. Technol. Lett. XXXX, XXX, XXX−XXX
Environmental Science & Technology Letters
Letter
(13) Sawama, Y.; Yabe, Y.; Shigetsura, M.; Yamada, T.; Nagata, S.; Fujiwara, Y.; Maegawa, T.; Monguchi, Y.; Sajiki, H. Platinum on Carbon-Catalyzed Hydrodefluorination of Fluoroarenes using Isopropyl Alcohol-Water-Sodium Carbonate Combination. Adv. Synth. Catal. 2012, 354, 777−782. (14) Baumgartner, R.; McNeill, K. Hydrodefluorination and hydrogenation of fluorobenzene under mild aqueous conditions. Environ. Sci. Technol. 2012, 46, 10199−10205. (15) Baumgartner, R.; Stieger, G. K.; McNeill, K. Complete hydrodehalogenation of polyfluorinated and other polyhalogenated benzenes under mild catalytic conditions. Environ. Sci. Technol. 2013, 47, 6545−6553. (16) McGregor, D. B.; Heseltine, E.; Møller, H. Dry cleaning, some solvents used in dry cleaning and other industrial chemicals. Scand. J. Work, Environ. Health 1995, 21, 310−312. (17) Ebnesajjad, S. Polyvinyl Fluoride; William Andrew, 2012. (18) Report on carcinogens: Carcinogen profiles. NTP 12th Report on Carcinogens; U.S. Department of Health and Human Services, Public Health Service, National Toxicology Program: Washington, DC, 2011; Vol. 12, pp 437−442. (19) Report on Carcinogens: Background Document for Vinyl Fluoride; U.S. Department of Health and Human Services, Public Health Service, National Toxicology Program: Washington, DC, 2005; pp 1−42. (20) Pirkanniemi, K.; Sillanpäa,̈ M. Heterogeneous water phase catalysis as an environmental application: A review. Chemosphere 2002, 48, 1047−1060. (21) Turner, J. C. R. Catalysis; Anderson, J. R., Boudart, M., Eds.; Springer-Verlag, 1981; Vol. 1, pp 43−86. (22) Arnold, W. A.; Ball, W. P.; Roberts, A. L. Polychlorinated ethane reaction with zero-valent zinc: Pathways and rate control. J. Contam. Hydrol. 1999, 40, 183−200. (23) Ranz, W. E.; Marshall, W. R. Evaporation from drops. Chem. Eng. Prog. 1952, 48, 141−146. (24) Harriott, P. Mass transfer to particles: Part I. Suspended in agitated tanks. AIChE J. 1962, 8, 93−101. (25) Goodman, A. L.; Bernard, E. T.; Grassian, V. H. Spectroscopic Study of Nitric Acid and Water Adsorption on Oxide Particles: Enhanced Nitric Acid Uptake Kinetics in the Presence of Adsorbed Water. J. Phys. Chem. A 2001, 105, 6443−6457. (26) Yan, B.-D.; Meilink, S.; Warren, G. W.; Wynblatt, P. Water Adsorption and Surface Conductivity Measurements on Alumina Substrates. IEEE Trans. Compon., Hybrids, Manuf. Technol. 1987, 10, 247−251. (27) Li, A.-J.; Nussinov, R. A set of van der Waals and coulombic radii of protein atoms for molecular and solvent-accessible surface calculation, packing evaluation, and docking. Proteins: Struct., Funct., Bioinf. 1998, 32, 111−127. (28) Atkins, P. W. Physical Chemistry, 4th ed.; Freeman: New York, NY, 1990; p 947. (29) Schwarzenbach, R. P.; Gschwend, P. M.; Imboden, D. M. Environmental Organic Chemistry, 2nd ed.; Wiley: Hoboken, NJ, 2003; pp 580−602.
E
dx.doi.org/10.1021/ez500291g | Environ. Sci. Technol. Lett. XXXX, XXX, XXX−XXX