Article pubs.acs.org/JPCC
Quantum-Chemical Study of the Diffusion of Hg(0, I, II) into the Ice(Ih) Abu Md. Asaduzzaman,†,§ Feiyue Wang,†,‡ and Georg Schreckenbach*,† †
Department of Chemistry and ‡Centre of Earth Observation Science, Department of Environment and Geography, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada § Lunar and Planetary Laboratory, Material Science and Engineering, University of Arizona, Tucson, Arizona 85721, United States ABSTRACT: A quantum-chemical study has been carried out to investigate the diffusion properties of mercury into the ice. The interstitial site for mercury is less stable than the surface site. The diffusion of mercury depends on its charge state. With strong charge, mercury has a smaller ionic radius and thus a lower diffusion barrier. Elemental mercury with its larger atomic radius has a higher diffusion barrier. The diffusion barrier correlates well with the nominal charge state on mercury. The rates of diffusion for the mercury ions (Hg+, Hg2+) are much higher than that of elemental mercury (Hg0).
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INTRODUCTION Mercury (Hg) can be transported over long distances and can biomagnify through the food chain. Recent studies have reported very high levels of Hg in marine mammals in the Arctic Ocean, raising concerns over the health of these animals and the Northern people.1 The discovery of photochemically driven, springtime atmospheric mercury depletion events (AMDEs) in the Arctic2 provides one mechanism of enhanced atmospheric mercury to the surface environment. However, at the time when AMDEs occur, the Arctic Ocean is primarily covered by sea ice and snow, and to which extent the AMDEdeposited Hg impinges on the underlying aquatic ecosystems remains a subject of scientific debate.3−5 Despite a recent fieldbased study on Hg partitioning and transport in the Arctic sea ice,4 fundamental physicochemical processes governing the Hg cycling in the ice environment are virtually unknown. One of the most common chemical processes that occur at the surface of ice is the adsorption of atoms, ions, and molecules, making the ice surface a potential reservoir of chemical contaminants in the cold environment6−12 As a first step toward a molecular-level understanding of Hg behavior in the ice environment, we have recently reported13 the results of a computational study of the adsorption of Hg atoms on an ice (Ih) surface and shown that the adsorption was dictated by the surface oxygen atom. We also found that Hg atoms bind very strongly on a defective ice surface but the binding is much weaker on the ideal ice surface due to the repulsion with surface H atoms. Here we extend the adsorption study by investigating the diffusion process of Hg into the ice (Ih) surface. The study of diffusion starts from the stable adsorbed position of mercury on the surface, as identified by our previous study.13 In addition to atomic Hg, we also considered different electronic charge states of Hg (+1 and +2). The diffusion path is identified, and the © 2012 American Chemical Society
diffusion barrier for various charge states is determined. Because of the computational limitations of modeling a charged state for the periodic system,14 a charge-balanced approached has been employed in this study. Thus, the charge states 1+ and 2+ have been modeled by employing the corresponding number of counterions (Cl−).
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COMPUTATIONAL PROCEDURE All calculations are performed by applying density functional theory (DFT) using plane-wave basis sets, as implemented in VASP (Vienna ab initio simulation package),15,16 version 4.6. The exchange-correlation contribution to the total energy is modeled using the GGA functional of Perdew and Wang (PW91).17,18 The electronic interactions are described by Vanderbilt ultra-soft pseudo potentials (US-PP)19 provided by VASP. The use of pseudopotentials also ensures that scalar relativistic effects are included in the calculations. The cutoff energy for the plane-wave expansion is set to 400 eV. For the number of k-points, we have used a 4 × 4 × 1 Mankhorst-Packk-points grid for the calculations. All calculations are performed in a periodically repeated simulation box of 8.88 Å × 7.72 Å × 30.28 Å, that is, the supercell approach. Previously13 optimized bulk parameters for ice(Ih) have been used in the supercell generation. The details of the optimization of the bulk parameters can be found in our previous study.13 Each supercell consists of five ice bilayers in a (2 × 2) periodic mode plus the adsorbed species (Figure 1) with the vacuum space of 15 Å for the bare surface and 12 Å for the adsorbed surface. Received: December 17, 2011 Revised: February 3, 2012 Published: February 7, 2012 5151
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Figure 1. Side view of one of the slabs used to model the ice surface (optimized structure). Red (green) circles denote O (H) atoms.
The convergence criterion for local energy minima is that all atomic forces be smaller than 0.02 eV/Å. The Hg atoms or ions are adsorbed at the bottom of the slabs. The Cl− ion is placed next to the H atoms at the other end of the slab. For two Cl− ions, they are placed as far as possible from each other. For both bare and adsorbed surfaces, atoms forming the center bilayer are kept in their bulk positions. All other atoms are allowed to relax. The details of the computational procedure can be found elsewhere.13 The reaction pathway and diffusion barriers are determined by using the constrained minimization along the corresponding reaction coordinate. The Bader charge20 analysis is performed based on the algorithm and code of Henkelman.21−23
Figure 2. Local adsorption and interstitial sites for Hg on the ice. (a,b) Sites A and B, respectively. (c) Interstitial site. The yellow spheres represent the adsorption and interstitial sites. The other presentation is as of Figure 1.
Table 1. Relative Stability (with respect to site B) and Barrier Heights (forward and backward reaction) of Different Adsorption and Interstitial (int.) Sites barrier height (eV)
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RESULTS AND DISCUSSION Two positions for Hgn+ (n = 0, 1, 2) surface adsorption have been considered, on top of an O atom (site A) and in the middle of the hexagon (site B),13 as shown in Figure 2. The Cl atom(s) (for Hg+ and Hg2+) were placed close to the H atoms, as already mentioned. For both Hg+ and Hg2+, the adsorption site B is more stable than site A. The energy differences between sites A and B for both cases are similar (0.11 eV), as shown in Table 1. The adsorption of Hg atoms has very similar energies on both sites. This might be due to the radius and charge of Hg in the adsorbed system, as discussed later. The bond distances between Hg and nearest neighbor O atoms are shown in the Table 2. Due to having only one nearest neighbor O atom, the Hg−O bond distances are significantly shorter at site A than those at site B. At site B, there are three nearest-neighbor O atoms. Hence the interaction between Hg and O atoms is divided into three pairs of interactions, and thus the average Hg−O bond distance is lengthened. However, the overall interaction in the site B is higher than that in the site A, and thus site B is more stable. The relative stability between the two sites can be rationalized from the strong electrostatic interactions between Hg and O atoms. The strong interaction results from the higher charge on Hg atoms on site B compared to site A for all Hg species, as can be seen from Table 3. The higher Bader charge on the site B for all Hg species clearly indicates stronger interactions with O atoms at site B, and thus we obtained that site B is more stable.
0
Hg Hg+ Hg2+
site A (eV)
site B (eV)
interstitial site (int.) (eV)
B to int.
int. to B
0.01 0.11 0.11
0.0 0.0 0.0
0.63 0.60 0.59
1.27 0.90 0.85
0.64 0.30 0.26
Table 2. Nearest-Neighbor Hg−O Distances (sites A and B) and Average Hg−O and Hg−H Distances over Six Nearest Neighbors (for the transition state from site B to the interstitial site) for the Adsorption of Hg, Hg+, and Hg2+ transition state (B to int. site) (Å) Hg0 Hg+ Hg2+
site A (Å)
site B (Å)
Hg−O
Hg−H
2.45 2.30 2.26
2.95, 3.18, 3.40 2.58, 2.78, 2.99 2.54, 2.73, 2.94
2.80 2.75 2.73
2.55 2.54 2.53
Next, we will discuss the diffusion of Hg into the ice slab. In principle, the Hg can diffuse from both stable surface adsorption positions (A and B) to the inside of the bulk ice (interstitial site). Given the binding pattern at Site A, it would need to first migrate to Site B before diffusing to the interstitial site. Therefore, we have first determined the diffusion barrier from site A to site B. Values of diffusion barriers for Hg0, Hg+, and Hg2+ are 0.047, 0.028, and 0.018 eV, respectively. These values are much smaller than their corresponding values from site B to the interstitial site (see in the next section). Such small 5152
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Hg−H distances (Table 2). For the transition states, the distances in Table 2 are presented as an average over six nearestneighbors. It is clearly seen that stronger Hg−O attractions lead to shorter Hg−O distances for the higher charged Hg species.
Table 3. Bader Charge (in electrons) on the Hg Atom in the Adsorption Sites A and B Hg0 Hg+ Hg2+
site A
site B
0.23 0.44 0.54
0.24 0.52 0.59
values indicate that the mercury species can hop between site A and site B with relative ease. To determine the local energy structures of Hg in the interstitial site, we have optimized the different Hg−ice systems placing the Hg inside the bulk. In the optimized structures, the Hg resides in the middle of two bilayers, as shown in the Figure 2. This is true for all charge states of Hg. It is only natural to rationalize this finding by noting that the interstitial sites are the largest vacant spaces available inside the bulk ice, having the least steric hindrance. Hence, the interstitial Hg position is lowest in energy. The interstitial site is, however, higher in energy than those on the surface (A and B). The relative stabilities among sites A, B, and interstitial site for all Hg species are presented in the Table 1. We have determined the diffusion barriers for all three species from Site B to the interstitial site. The diffusion barriers for all three species are shown in Figure 3. The diffusion barriers for Hg0, Hg+, and Hg2+ are 1.27, 0.90, and 0.85 eV with respect to site B and 0.64, 0.30, and 0.26 eV with respect to the interstitial site, respectively. The calculated diffusion barriers depend on the charge states of the diffusing atom (Hg in this case). The neutral Hg atom with 0 charge is having the largest ionic radius among the three species. The large ionic radius (atomic radius for Hg) induces the largest steric repulsion with the neighboring atoms resulting in the highest energy and thus the highest diffusion barrier. The ionic radius is decreasing with increasing the charge on Hg.
Figure 4. Variation of ionic radius24 (in nanometers), diffusion barrier (in electronvolts), and Bader charge (in electrons) with the charge state of Hg.
However, the Hg−H distance changes relatively little from 0 to 2+ charge of Hg. Although the diffusion barrier for Hg0 is markedly different from those for Hg+ and Hg2+, the relative stability in the interstitial site for the three species is not so different. One of the reasons for this observation is that the steric interactions in the diffusion path are higher than those in the interstitial site. In the interstitial site, the H atoms are far away from the Hg atoms or ions, whereas the H atoms are close to the Hg species in the diffusion path. Another reason for this observation is the charge on the Hg. The higher the charge on Hg, the larger the repulsion with hydrogen atoms. However, the nominal charge on an impurity atom is not directly comparable to the calculated atomic charges. We also note that calculated atomic charges are not observable quantities in a quantum-mechanical sense. In the experimental setup, the charge state of any impurity is based on the ions with integer charge and free carriers. However, in the first-principle calculation, the charge state of the impurity is defined by fixing the total number of electrons for the supercell. The actual charge on the impurity has a different value, which is obtained by the self-consistent solution of the electronic structure problem. For example, for the Hg0 nominal state, we have obtained a Bader charge of 0.24 at site B. Put differently; the nominally neutral Hg0 is actually a cation with a partial positive charge. The electronic charge missing on the Hg site is distributed over the supercell. The distributed charge may be localized or delocalized in nature. Similarly, Bader charges for the nominal Hg+ and Hg2+ are 0.52 and 0.59, respectively. Only a slight charge difference is obtained for the nominal charges of Hg+ and Hg2+. Whereas it might be difficult to describe accurately the nominal charge theoretically, we have, however, obtained a correlation between charge and diffusion barrier, as shown in Figure 4. The variation of the Bader charge for all Hg species is nonlinear in nature and so is our calculated diffusion barrier (in the opposite direction). Therefore, we have obtained a qualitative description of a model for the diffusion of Hg into the bulk ice; that is, the higher the charge on the Hg, the smaller the diffusion barrier.
Figure 3. Diffusion barrier from the adsorption site B to the interstitial site for the diffusion of Hg0 (▲), Hg+ (◆), and Hg2+(●). The energy for site B is considered to be zero for all species.
The barrier height−charge state profile can be correlated to the ionic radius−charge state profile. Very similar characteristic features (nonlinear) for both of them can be seen from Figure 4. With smaller ionic radii, the Hg has less steric interactions and thereby lower diffusion barriers. The electronic nature of the diffusing species also plays a role in stabilizing the transition state. There are two types of forces that are acting on the Hg; attractive forces with O atoms and repulsive forces with H atoms. The attractive forces dominate over the repulsive forces. This can be seen from the nearest-neighbor Hg−O and 5153
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Hg with higher charge and the rate can be expected to increase with higher temperature. The characteristic features of Hg diffusion will aid the research on how and why Hg is transported across the Earth’s cryosphere such as the sea ice environment in the polar oceans.
The diffusion coefficient can be defined as D=
1 kT f
(i)
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where f is frictional coefficient, k is Boltzmann’s constant, and T is absolute temperature. The frictional coefficient is f = 6πσr
(ii)
The authors declare no competing financial interest.
where σ is viscosity of the medium and r is radius of the solute. The determination of the viscosity of ice is not trivial. We can, however, estimate the coefficient of Hg by approximating the viscosity of ice. Using a value for the viscosity of ice of unity at a temperature of 0 °C, the calculated values of D for Hg0, Hg+, and Hg2+ are 1.17 × 10−12, 1.50 × 10−12, and 1.72 × 10−12 cm2 s−1, respectively. The diffusion coefficient is higher with a smaller radius, in line with our observation above. To the best of our knowledge, there are no data available for diffusion coefficients in similar types of systems. However, there are some experimental data (ref 25 and reference therein) available for simple molecules (mainly organic) and for Na atoms. The diffusion coefficients for Na atom and HCl in the bulk ice are reported as 1.1 × 10−12 to 4.5 × 10−10 and 2.0 × 10−13 to 1.1 × 10−10 cm2 s−1, respectively. Our calculated values are within the range of these experimental reports. The rate of diffusion and dependence of the diffusion on temperature can be explained using a simple Arrhenius equation k′ = Ae−ΔE / kT
AUTHOR INFORMATION
Notes
ACKNOWLEDGMENTS We would like to acknowledge funding from The EJLB Foundation (http://www.ejlb.qc.ca/), the Natural Sciences and Engineering Research Council of Canada (NSERC), and the University of Manitoba (University Research Grants Program, URGP). All calculations were performed using the Atlantic Computational Excellence Network (ACEnet). ACEnet is supported by CANARIE.
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REFERENCES
(1) AMAP 2011, AMAP Assessment 2011: Mercury in the Arctic; Arctic Monitoring and Assessment Program: Oslo, Norway, 2011. (2) Schroeder, W. H.; Anlauf, K. G.; Barrie, L. A.; Lu, J. Y.; Steffen, A.; Schneeberger, D. R.; Berg, T. Nature 1998, 394, 331. (3) Wang, F.; Macdonald, R. W.; Stern, G. A.; Outridge, P. M. Mar. Pollut. Bull. 2010, 60, 1633. (4) Chaulk, A.; Stern, G. A.; Armstrong, D.; Barber, D.; Wang, F. Environ. Sci. Technol. 2011, 45, 4566. (5) Outridge, P. M.; Macdonald, R. W.; Wang, F.; Stern, G. A.; Dastoor, A. P. Environ. Chem. 2008, 5, 89. (6) Bolton, K. J. Mol. Struct.: THEOCHEM 2003, 632, 145. (7) Brown, A. R.; Doren, D. J. J. Phys. Chem. B 1997, 101, 6308. (8) Clary, D. C.; Wang, L. J. Chem. Soc., Faraday Trans. 1997, 97, 2763. (9) Hara, Y.; Hashimoto, N. T.; Nagaoka, M. Chem. Phys. Lett. 2001, 348, 107. (10) Hashimoto, N. T.; Hara, Y.; Nagaoka, M. Chem. Phys. Lett. 2001, 350, 141. (11) Thierfelder, C.; Hermann, A.; Schwerdtfeger, P.; Schmidt, W. G. Phys. Rev. B 2006, 74, 045422. (12) Thierfelder, C.; Schmidt, W. G. Phys. Rev. B 2007, 76, 195426. (13) Asaduzzaman, A. M.; Schreckenbach, G. J. Phys. Chem. C 2010, 114, 2941. (14) Asaduzzaman, A.; Schreckenbach, G. Phys. Chem. Chem. Phys. 2010, 12, 14609. (15) Kresse, G.; Furthmüller, J. Comput. Mater. Sci. 1996, 6, 15. (16) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758. (17) Perdew, J. P. Electronic Structure of Solids ’91; Akademie-Verlag: Berlin, 1991. (18) Perdew, J. P.; Wang, Y. Phys. Rev. B 1992, 45, 13244. (19) Kresse, G.; Hafner, J. J. Phys.: Condens. Matter. 1994, 6, 8245. (20) Bader, R. F. W. Atoms in Molecules - A Quantum Theory; Oxford University Press: Oxford, U.K., 1990. (21) Henkelman, G.; Arnaldsson, A.; Jónsson, H. Comput. Mater. Sci. 2006, 36, 254. (22) Sanville, E.; Kenny, S. D.; Smith, R.; Henkelman, G. J. Comput. Chem. 2007, 28, 899. (23) Tang, W.; Sanville, E.; Henkelman, G. J. Phys.: Condens. Matter 2009, 21, 084204. (24) http://www.webelements.com/. (25) Livingston, F. E.; Smith, J. A.; George, S. M. J. Phys. Chem. A 2002, 106, 6309. (26) Asaduzzaman, A. M; Kruger, P. Phys. Rev. B 2007, 76, 115412.
(iii)
where ΔE is the diffusion barrier and A is the Arrhenius constant. Using a typical value of A,26 we can calculate the rate of diffusion at a temperature of 0 °C. The calculated values for Hg0, Hg+, and Hg2+ are 15.2, 2.87 × 107 and 1.58 × 108 s−1, respectively. The rate of diffusion is higher for strongly charged Hg. This is also related to our previous explanation of the charge and ionic radius-dependent diffusion of Hg. From the Arrhenius equation, it can easily be seen that with increasing temperature the rate of diffusion will be higher. We should note, however, that in the case of ice in nature, the actual rate of diffusion will largely depend on the structure of the ice and impurities contained within. Furthermore, diffusion in sea ice is much more different due to the presence of surface water layers, defects, and, in particular, highly concentrated brine drainage and interstitial air. A description of Hg diffusion in such complicated natural systems is beyond the scope of the current paper. Nevertheless, we have established a relationship between the diffusion properties of Hg and the charge state, ionic behavior, and temperature, which will guide in elucidating the dynamic behavior of Hg in the pure ice.
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CONCLUSIONS The adsorption on and diffusion into the ice depend largely on the charge of Hg. With stronger charge on Hg, there is a stronger force of attraction between Hg and surface oxygen atoms, resulting in shorter Hg−O bond distances. The Hg species with the highest positive charge has a lower ionic radius compared with those with lower (1+) or zero charges. The smaller the radius of Hgn+, the easier it is to diffuse through into the bulk. The easier diffusion corresponds to a lower diffusion barrier. The diffusion barrier and calculated Bader charge are correlated with the ionic radius if taken as functions of the formal Hg charge. The diffusion coefficient further confirms the lower diffusion barrier for higher charged Hg. The rate of diffusion is higher for 5154
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