Environ. Sci. Technol. 2009, 43, 3183–3186
An Elemental Mercury Diffusion Coefficient for Natural Waters Determined by Molecular Dynamics Simulation ¨ RG HOLZMANN,‡ J O A C H I M K U S S , * ,† J O AND RALF LUDWIG‡ Department of Marine Chemistry, Leibniz Institute for Baltic Sea Research (IOW), Seestrasse 15, D-18119 Rostock-Warnemu ¨ nde, Germany, and Theoretical and Physical Chemistry, Institute for Chemistry, University of Rostock, Dr.-Lorenz-Weg 1, D-18059 Rostock, Germany
Received December 9, 2008. Revised manuscript received February 24, 2009. Accepted March 5, 2009.
Mercury is a priority pollutant, as its mobility between the hydrosphere and the atmosphere threatens the biosphere globally. The air-water gas transfer of elemental mercury (Hg0) is controlled by its diffusion through the water-side boundary layer and thus by its diffusion coefficient, DHg, the value of which, however, has not been established. Here, the diffusion of Hg0 in water was modeled by molecular dynamics (MD) simulation and the diffusion coefficient subsequently determined. Therefore the movement of either Hg0 or xenon and 1000 model water molecules (TIP4P-Ew) were traced for time spans of 50 ns. The modeled DXe of the monatomic noble gas agreed well with measured data; thus, MD simulation was assumed to be a reliable approach to determine DHg for monatomic Hg0 as well. Accordingly, Hg0 diffusion was then simulated for freshwater and seawater, and the data were well-described by the equation of Eyring. The activation energies for the diffusion of Hg0 in freshwater was 17.0 kJ mol-1 and in seawater 17.8 kJ mol-1. The newly determined DHg is clearly lower than the one previously used for an oceanic mercury budget. Thus, its incorporation into the model should lead to lower estimates of global ocean mercury emissions.
Introduction Mercury is a pollutant of major concern due to the fact that, after its emission from anthropogenic sources, the elemental mercury (Hg0) fraction is subject to long-range atmospheric transport and, consequently, deposition elsewhere on the planet. Mercury is exchanged between the atmosphere and the hydrosphere and is easily transformed by chemical or biological processes to numerous speciations (1-3). Moreover, toxic organic mercury compounds accumulate in the aquatic (4, 5) and the terrestrial (6) food chain. The release of mercury from anthropogenic point sources is restricted by emission control regulations. However, soils (7, 8) and large water surfaces (9-11) of the Earth have become longterm repositories of the metal, and their diffuse Hg0 emissions are difficult to quantify. Water-air fluxes of mercury have * Corresponding author phone: +49-(0)381-5197-314; fax: +49(0)381-5197-302; e-mail:
[email protected]. † Leibniz Institute for Baltic Sea Research (IOW). ‡ University of Rostock. 10.1021/es8034889 CCC: $40.75
Published on Web 03/26/2009
2009 American Chemical Society
been determined directly by flux chambers (12, 13) or calculated based on measured air-sea concentration differences and the air-water gas transfer velocity (14-18). The frequently used latter method requires a coefficient for the diffusion of Hg0 (DHg) in water. Because for sparingly soluble Hg0 (19, 20) the water-side boundary layer controls the passage across the interface (21). Unfortunately, however, DHg has not been measured. Air-water Gas Exchange. At the air-water interface, the solubility of a gas determines its equilibrium distribution, while the speed of the exchange process is a function of the gas’ diffusion through the interface. In geochemical studies, the air-water gas flux (F) is mostly calculated from the concentration difference between air and water ∆cair-water and the gas-exchange transfer velocity k (22): F ) k*∆cair-water
(1)
This approach was originally conceived for the film model (23), but it is also applicable to other models describing the air-sea interface with otherwise defined values of k (24). In practice, empirical equations are used in which k is described as a function of wind speed (u), with the k(u) usually given for CO2 at 20 °C either in freshwater (Schmidt number, Sc)600 (25)) or in seawater (Sc)660, e.g. 26-28). The parametrization is then adapted to other gases and temperatures by accounting for the deviating Schmidt numbers (Sc ) ν/D), the ratio of the kinematic viscosity of water (ν), and the diffusivity of the respective gas. Hence, k can be calculated for different gases at various water temperatures as follows: k(u) ) k600(u)·(Sc/600)-n
(2)
with n ) 0.5 mostly used for environmental applications. In previous studies, the Hg0 diffusion coefficient and the ScHg were estimated by two principal but different approaches. Mass-Based Approximation. Liss and Slater assumed that, for various low-molecular-weight gases (22), k is inversely proportional to the square root of the molecular mass (mMol). Hence, Sc is proportional to mMol and D is inversely proportional to mMol (eq 2 with n ) 0.5). This was then applied by Schroeder et al. (17) to Hg0. If the findings for gas kinetics were valid for aqueous medium, then D would be inversely proportional to the square root of the molecular mass (m), as was shown for rare gases (29) and applied to lowmolecular-weight halocarbons (30). The aqueous diffusion coefficients of monatomic gases measured previously (29) were plotted as a function of mass (Figure 1a). The fit revealed a power dependency to the -0.464. This roughly corresponds to an inverse proportionality to the square root of the molecular mass, similar to the findings in the gas phase. From this perspective, the kinetic energy of the translational motion of the molecules seems to determine their diffusion. Volume-Based Approximation. A widely used approximation for DHg and its temperature dependence is based on the Wilke-Chang methodology, in which the diffusion coefficient is inversely proportional to the 0.6th power of the molecular volume VMol (31, 32). For organic compounds, the correlation proved to give reliable estimates of D (32, 33) such that it was also applied to Hg0 in some studies (14, 18, 34). The measured D of selected small gas molecules (29, 33) versus the molecular volume to the 0.6th power is plotted in Figure 1b. Data for the molecular volumes, calculated from the liquid density, were taken from ref 33. Another volumebased approximation for DHg was used in the first study of ocean mercury emissions (16), in which the authors included VOL. 43, NO. 9, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. DHg obtained by MD simulation (solid circles) with the fit DHg)0.01768 * exp((16.98 kJ mol-1)/RT) for freshwater (thick solid line) and DHg)0.02293 * exp((17.76 kJ mol-1)/RT) for seawater (open squares, thin solid line) compared to estimated DHg according to the Wilke-Chang method (18) (dotted line) and by application of a mass-based approximation (17, 22) (dashed line). Data are given for liquid water only.
Methods FIGURE 1. a) The diffusion coefficients of monatomic gases at 25 °C (29) versus their molecular mass (mMol) is fitted by a potential function: D25 (10-5 cm2 s-1) ) 14.69 mMol-0.464 (solid line); the value for Rn (diamond) was calculated by Ja¨hne et al. (29); an estimate for DHg based on the fit is also plotted (open circle with data pair). b) Diffusion coefficients of He, H2 (small solid diamonds), Ne, Kr, Xe, CH4, and CO2 at 25 °C (29) and of Ar, O2, CO, and H2O (33) plotted (solid squares) versus molecular volume (VMol) to the 0.6th power with the fit: D25 (10-5 cm2 s-1) ) -0.49*VMol0.6 + 6.06; He and H2 are excluded from the fit; in addition, an estimate for DHg based on the fit is shown (open circle with data pair).
FIGURE 2. The diffusion coefficient of Xe versus temperature as obtained from MD simulation (solid squares with bars of 1σ) and fitted by the Eyring curve (solid line) DXe)0.03936 * exp((19.60 kJ mol-1)/RT); a comparison to Xe measurements (open circles), with the fit (dashed line) DXe)0.09007 * exp((21.61 kJ mol-1)/RT) as determined by Ja¨hne et al. (29), is also shown. Data are given for liquid water only. the Othmer-Thakar (35) equation in their calculations. The Othmer-Thakar method results in a DHg that is slightly smaller than the DHg deduced by the Wilke-Chang methodology. A simple linear parametrization of the coefficient leads to a DHg that is reduced even further and is closer to the mass-based approximation. It was used by Poissant et al. (36), referenced to Thibodeaux (37). It seems that all approximations are somehow justified and reliably describe measurements under certain prerequisites. However, for Hg0, unacceptable deviating values for the diffusion coefficient are obtained by the various methods since elemental mercury consists of small and heavy atoms. As a new approach is urgently needed to address these discrepancies, in the present study we have used a molecular dynamics (MD) simulation to optimize the DHg estimate. 3184
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Molecular Dynamics Simulations. The molecular dynamics of the aqueous solution (38) were simulated with a system of 1000 TIP4P-Ew model water molecules (39) and a time period of 50 ns. The model water phase was spiked with mercury (Hg0) or xenon (Xe) atoms, i.e., with particles having the following potential parameters: xenon (σXe ) 3.975Å, εXe kB-1 ) 214.7 K) (40) and mercury (σHg ) 2.969Å, εHg kB-1 ) 750 K) (31). Hg diffusion was also simulated for an aqueous salt solution after including 11 ion pairs of Na+ and Cl-: sodium chloride (σNa+ ) 0.273 nm, εNa+kB-1 ) 43.06 K, σCl) 0.486 nm, εCl-kB-1 ) 20.21 K) (41). The NaCl content of 3.55 w% approximately represented water of oceanic salinity. Briefly, the applied procedures were as follows: Standard Lorentz-Berthelot mixing rules were employed to determine the Lennard-Jones cross-interactions. A smooth-particlemesh Ewald method (42) was used to solve the electrostatics, according to the same setup as described by Paschek (43). Long-range corrections for pressure and energy were taken into account. All simulations were carried out by the GROMACS 3.2 simulation program (44). Bond-length constraints were solved by means of the SETTLE procedure (45). The simulations were performed under isobar isothermal conditions using a Nose´-Hoover thermostat (46, 47) and a Rahman-Parrinello barostat (48, 49) with coupling times of τT ) 1.0 ps and τP ) 2.0 ps; the MD time step was ∆t ) 2.0 fs. Each diffusion coefficient D was obtained from the asymptotic slope of the mean-square displacement of the mercury or xenon atoms within the ensemble of water molecules versus time: D)
1 〈|r (t) - ri(0)| 2〉 6t i
(3)
Results and Discussions Molecular dynamics simulations for the movement of xenon and mercury in water were determined for a temperature range between 260 and 330 K. The simulation was extended to the range of supercooled water to improve the precision of the fit. Xenon was selected as the reference because reasonable measured data are available. Moreover, Xe is a monatomic gas with a high molar mass of 131.3 g, and its behavior in solution is probably comparable to that of Hg0. It is obvious from Figure 2 that modeled data of Xe are in excellent agreement with measured data (29). Diffusion Characterized by Its Activation Energy. Ja¨hne et al. (29) proposed using the concept of Eyring (50) as a reliable description of the dependency of D on absolute temperature (T). It is based on control of the diffusion process by an activation energy (Ea). Thus, the frequency of changing
TABLE 1. Comparison of the Parameters Ea and A of the Eyring Equation (Eq 4) for the Modeled (Hg0 and Xe) and Measured (Xe) Diffusion Coefficients in Water (this study)
Ja¨hne et al. 1987
fresh water
gas
EaMD (kJ mol-1)
AMD (cm2 s-1)
Eameas (kJ mol-1)
Ameas (cm2 s-1)
Hg0 (fresh water) Hg0 (seawater) Xe (fresh water)
16.98 17.76 19.60
0.01768 0.02293 0.03936
21.61
0.09007
position for the respective atom in bulk water is increased at higher temperatures according to eq 4: D ) A·e
-Ea/ RT
TABLE 2. Calculated Mercury Diffusion Coefficients and Schmidt Numbers (Sc = ν/DHg) for Fresh Water and Seawater at Corresponding Water Temperatures (Eq 4 with Ea and A from Table 1)
(4)
The data from MD simulations were fitted by plotting Ln(D) versus 1/T, which revealed an Ea of 19.6 kJ mol-1 for xenon. This is in good agreement with the measured Ea of 21.6 kJ mol-1 determined by Ja¨hne et al. (29). The coefficient of variation was about 5%. The fit to the measured data was extrapolated to the same temperature range, from 260 to 330 K, for a better comparison with the MD simulation results. For elemental mercury, the fit gave an Ea of 16.98 kJ mol-1 for the diffusion of Hg0 in freshwater and 17.76 kJ mol-1 for the diffusion in seawater (Table 1, Figure 3). Thus, compared to freshwater, the diffusion of Hg0 in seawater was about 8% lower at 0 °C and 4% lower at 40 °C. This is in agreement with expectations, as discussed for other gases (51), because the viscosity of seawater at 15 °C is ∼6-7% higher than that of pure water. The estimated diffusion coefficients based on mass and molecular volume were determined for an environmental temperature range of 0-40 °C. The deviations between the different approaches are striking. The MD simulation results lay in the middle between those obtained with the volume and the mass approximations. Hence, both molecular mass and molecular volume determine the diffusion of mercury in water. Interestingly, using Ea)19.51 kJ mol-1 and A)0.005019 cm2 s-1 for CO2, as determined by Ja¨hne et al. (29), the curve of DHg versus temperature of our study was close to the curve of CO2 (Figure 4) between 10 and 25 °C and deviated beyond this range. Thus, only a small error is introduced if a transfer velocity (k) parametrization that is usually given for CO2 is directly applied to Hg0 (52). In Table 2 the values of DHg and of the Hg0 Schmidt number for fresh water and seawater are given for selected temperatures. Thus, with the data of Table 2 and eq 2 an improved adaptation of k for Hg0 at various environmental conditions can be done.
seawater
T (°C)
DHg (10-5 cm2 s-1)
Sca
DHg (10-5 cm2 s-1)
Scb
0 5 10 15 20 25 30
1.00 1.15 1.31 1.48 1.67 1.88 2.10
1783 1325 1002 771 601 476 381
0.92 1.06 1.21 1.38 1.57 1.77 1.99
2046 1520 1150 884 689 545 434
a Data of the kinematic viscosity (ν) were used as given by Schwarzenbach et al. (53). b The kinematic viscosity of fresh water (53) was multiplied by a factor parametrized by Wanninkhof (27).
Impact on a Previous Budget. To discuss the impact of the newly determined Hg0 diffusion coefficient, the global oceanic mercury budget given by Strode et al. (9) was chosen as the reference system. The authors were the first to calculate a global ocean Hg0 emission estimate, based on a comprehensive model for the atmosphere and the surface ocean. They obtained a net evasion flux of 14.1 Mmol Hg0 yr-1 (9) based on an approximation of DHg from Poissant et al. (36). Our DHg calculated from MD simulations was in agreement with their value at 0 °C (the temperature in polar regions) but 24% lower at 30 °C (the temperature in the equatorial region), as shown in Figure 4. Hence, changes in the oceanic Hg0 emission budget resulting from calculations incorporating the new DHg are expected to be significant. The spatial and seasonal variability of the temperature distribution as well as the Hg0 sink and source regions of the oceans make a quick estimate of the impact difficult. However, since increased temperatures are frequently coupled to higher oceanic Hg0 emissions, i.e., large areas of the tropical and subtropical oceans are likely characterized by high oceanic Hg0 emissions (9), the global oceanic emission estimate should be scaled down by at least 10%.
Acknowledgments We gratefully acknowledge the funding of the German Science Foundation (DFG) and the financial support of the Federal Ministry of Education and Research of Germany in the frame of the “Pact for Research and Innovation” of the Leibniz Science Association.
Supporting Information Available Data of the mercury diffusion coefficient and for comparison of xenon as determined by molecular dynamics simulation (Table S1).This material is available free of charge via the Internet at http://pubs.acs.org.
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FIGURE 4. Comparison of DHg in freshwater (this study, solid line) with the parametrization for DHg of Poissant et al. (36) as a dashed line; DCO2 determined by Ja¨hne et al. (29) for freshwater (dotted line) DCO2)0.05019*exp((19.51 kJ mol-1)/RT) is also shown.
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