Molecular Simulations of Water and Ion Diffusion in Nanosized

Jan 9, 2009 - Molecular dynamics simulations were carried out to investigate the effects of confinement and of the presence of the mineral surface on ...
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Environ. Sci. Technol. 2009, 43, 777–782

Molecular Simulations of Water and Ion Diffusion in Nanosized Mineral Fractures SEBASTIEN KERISIT* AND CHONGXUAN LIU Chemical and Materials Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352

Received June 11, 2008. Revised manuscript received November 17, 2008. Accepted November 26, 2008.

Molecular dynamics simulations were carried out to investigate the effects of confinement and of the presence of the mineral surface on the diffusion of water and electrolyte ions in nanosized mineral fractures. Feldspar was used as a representative mineral because recent studies found that it is an important mineral that hosts contaminants within its intragrain fractures at the U.S. Department of Energy Hanford site. Several properties of the mineral-water interface were varied, such as the fracture width, the ionic strength of the contacting solution, and the surface charge, to provide atomiclevel insights into the diffusion of ions and contaminants within intragrain regions. In each case, the self-diffusion coefficient of water and that of the electrolyte ions were computed as a function of distance from the mineral surface. Our calculations reveal a 2.0-2.5 nm interfacial region within which the self-diffusion coefficient of water and that of the electrolyte ions decrease as the diffusing species approach the surface. As a result of the extent of the interfacial region, water and electrolyte ions are predicted to never reach bulklike diffusion in fractures narrower than approximately 5 nm. The average diffusion coefficient along the mineral fracture was computed as a function of fracture width and indicated that the surface effects only become negligible for fractures several tens of nanometers wide. The molecular dynamics results improve our conceptual models of ion transport in nanoscale pore regions surrounded by mineral surfaces in porous media.

Introduction The macroscopic diffusive flux of ions and molecules in porous media is often assumed to be proportional to the bulk diffusivity modified by several factors such as the medium porosity, constrictivity, and tortuosity (1). Porosity represents the fraction of the media accessible to the solution; constrictivity takes into account the decrease in diffusivity due to the variation in pore and diffusant sizes, whereas tortuosity accounts for the deviation of the length of the path of a tracer molecule from that of a straight line. Dykhuizen and Casey (2) extended the concept of tortuosity to include the effects of the distribution of pore sizes and lengths, the number of pores that intersect at a node, and the pore shape between nodes. However, one component generally ignored or incorporated as an indiscernible part of geometrical factors is the effects of the mineral-fluid * Corresponding author e-mail: [email protected]. 10.1021/es8016045 CCC: $40.75

Published on Web 01/09/2009

 2009 American Chemical Society

interactions on the diffusion coefficient of a particular species. Indeed, both experimental techniques (3) and molecular simulations (4-6) have shown the presence of an interfacial water region at the mineral-water interface that is structurally and dynamically different from the bulk. For example, in a previous study (7), we showed that interfacial electron density profiles, computed from molecular dynamics (MD) simulations of water in contact with the (001) and (010) surfaces of the feldspar mineral orthoclase, revealed the presence of two to three distinct and ordered water monolayers at the interface. The computed electron density profiles were in good agreement with those derived previously from highresolution X-ray reflectivity measurements by Fenter and co-workers (8), indicating that the molecular model provides an adequate representation of the structural properties of the orthoclase-water interface and giving us confidence in employing such a model for calculating self-diffusion coefficient profiles. The idea that the reduced mobility of water near a mineral surface, in media with a significant fraction of nanopores, needs to be accounted for has already emerged in the literature. For example, Bourg et al. (9) have addressed this concept in their work modeling tracer diffusion in compacted, water-saturated bentonite. Another example that emphasizes the importance of mineral-water interactions in confined systems is the phenomenon of supercooled confined aqueous solutions, whereby the nucleation temperature of aqueous solutions can be depressed when confined (10). In particular, neutron scattering techniques have been used extensively for studying this phenomenon (10, 11). Therefore, in this study, we use MD simulations to investigate whether molecular-scale fluctuations in the structure of water at the mineral-water interface can significantly affect the overall diffusion of water and ions within nano- to microsized fractures. When used to determine the water self-diffusion coefficient in the interfacial region, MD simulations have consistently shown a decrease with decreasing distance to the surface (4-6, 12). In this report, we extend upon this general finding by quantifying the effects of several parameters, such as the pore width, the ionic strength, and the surface charge, on the diffusion coefficient of water and electrolyte ions. Also, by extrapolating the MD results to larger widths, we determine the critical thickness at which the mineral surface effects become negligible. Intragrain fracture regions of the mineral orthoclase were used as an example of such nanosized porous regions. Recent spectroscopic and microscopic studies of contaminated sediments from the U.S. Department of Energy Hanford Site have revealed that feldspar is an important mineral that preferentially sequestered U(VI), from the contaminated waste solutions, in its nano- to microsized intragrain fractures (13, 14). Diffusion measurements and modeling indicated that the slow uranium diffusion led to the preferential U(VI) association in the feldspar intragrain microfractures. Furthermore, intragrain diffusion was predicted to be an important process regulating the future release of U(VI) from the contaminated sediment as a secondary long-term source to pore and ground waters (15). One general aim of this work is to provide atomic-level insights for the contribution of microscopic surface effects to the slow diffusion process in porous media.

Computational Methods Orthoclase (KAlSi3O8) is the potassium end-member of alkali feldspar, a framework silicate. Corner sharing AlO4 and SiO4 VOL. 43, NO. 3, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 2. Water diffusion coefficient as a function of distance for three pore widths. Water density is also shown for L ) 10.0 nm. All surfaces are uncharged. The horizontal solid line represents the water diffusion coefficient obtained from a separate bulk calculation. The mineral surfaces are positioned at 0.0 nm for all three widths, and at 2.66, 5.16, and 10.16 nm for the 2.5, 5.0, and 10.0 nm widths, respectively.

FIGURE 1. Schematic of a typical MD simulation cell where L ) 2.5 nm. Si atoms are shown in yellow, Al atoms in gray, potassium atoms in green, oxygen atoms in red, and hydrogen atoms in white. The horizontal lines show the position of the surfaces (x ) 0 in subsequent figures). tetrahedra form a three-dimensional lattice within which alkali cations fill cavities to compensate for the charge deficiency due to Al substitution for Si. Previous work (7) on the (001) and (010) surfaces showed good agreement with the X-ray reflectivity data of Fenter and co-workers (8) on the interface structure. Our simulations, in this paper, focus on the (001) surface, but the results are similarly applicable to the other surface. The (001) slab was generated as described previously (7) and is terminated by a full layer of hydroxyl groups. The surface area was 2.569 × 2.693 nm2. The surface (i.e., zero distance in Figures 2, 3, and 5-7 shown later) was defined as the plane that passes through the topmost Si/Al tetrahedral sites (Figure 1 ). The direction normal to the surface was extended to introduce a sodium chloride solution of varying concentration. Three-dimensional periodic boundary conditions were applied, meaning that the thickness of the fracture is finite in one direction and infinite in the other two directions (Figure 1). The extent of the water slab in the finite dimension will be referred to as the pore or fracture width, L. Three fracture widths were considered, namely 2.5, 5.0, and 10.0 nm. In addition, four sodium chloride solutions of concentration 0.00, 0.25, 0.50, and 1.00 mol · dm-3 were simulated for each pore width. Finally, negatively charged surfaces were generated by deprotonating surface hydroxyl groups. Two surface charges (-7.2 and -14.4 µC · cm-2) were considered for the 5.0 nm pore width. In both cases, the net charge of the surface was neutralized by adding sodium ions to the solution. Although these surface charges were chosen to probe the effects of surface charge on diffusion rather than for modeling specific conditions, we note that the work of Stillings et al. (16) on the titration of an adularia feldspar powder suspension indicates that the surface charges used in this work are bracketed by the surface charges that develop due to protonation/deprotonation of surface groups between approximately pH 7 and pH 10. 778

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The MD simulations were carried out with the computer code DL_POLY (17). In these calculations, atoms are represented as point-charge particles that interact via long-range Coulombic forces and short-range interactions. The latter are described by parameterized functions and represent the repulsion between electron-charge clouds, the van der Waals attraction forces, and many-body terms such as bond bending. The short-range potential parameters and ionic charges used in this work are those of the SPC/E model (18) for water and those of the CLAYFF force field (19) for the solid phase. A series of modifications to the CLAYFF force field was introduced in a previous publication (7) to ensure that the potential parameter set for the solid phase was consistent with the potential models of sodium and potassium chloride solutions. All the potential parameters and ionic charges used in this work are reported in the Supporting Information. The simulation procedure followed that described in a previous publication (7). In particular, all the simulations were carried out at 300 K and the atomic velocities were initially scaled for 100 ps to the target temperature followed by data collection for 10 ns. For each simulation, a selfdiffusion coefficient profile was computed. The diffusion coefficient, D, was obtained from the mean square displacement (MSD): 1 2Dt ) 〈|ri(t) - ri(0)|2 〉 n

(1)

where ri(t) is the position of atom i at time t and n is the number of dimensions in which the diffusion is considered. Unless otherwise noted, all the diffusion coefficient profiles computed in this work are those in the direction parallel to the surfaces. Therefore, only the atomic coordinates in the direction parallel to the surface are considered (i.e., x and y if z is the normal to the surface) and n equals 2. The only exceptions are the water diffusion coefficient profile in the direction normal of the surface shown in Figure 3, for which only the atomic coordinates in the direction normal to the surface are considered and n equals 1; and the water bulk diffusion coefficient, for which no distance dependence is considered and n equals 3. Moreover, the water diffusion coefficients are determined from the oxygen ion positions. A configuration was recorded every 0.2 ps for calculating the diffusion coefficients. As water molecules explore regions with different diffusion coefficients within the time-scale of the simulations, the MD trajectories were divided into shorter

FIGURE 3. Water diffusion coefficient in the directions normal and parallel to the surface and water density in the interfacial region (L ) 5.0 nm, uncharged surface). 10-ps trajectories. Each recorded configuration was used as the origin of a new 10-ps trajectory and the geometric center of the trajectory was used to determine where to bin the value of the MSD along the normal to the surface. Therefore, for a typical 10-ns simulation, the diffusion coefficient profile of a species i was constructed using 50,000 × Ni 10-ps trajectories, where Ni is the number of species i. The bin width used along the normal to the surface was 0.02 nm.

Results and Discussion The effect of the pore width, L, on the distance dependence of the self-diffusion coefficient of water was first evaluated for the case where the orthoclase fracture is filled with pure water. Water has been experimentally used as a tracer to determine diffusion properties within intragrain feldspar pore regions using nuclear magnetic resonance (15). Three pore widths were considered: 2.5, 5.0, and 10.0 nm, and the distance dependence of the water diffusion coefficient in these three fractures is shown in Figure 2. The water density profile from the simulation with L ) 10.0 nm is also shown and indicates the presence of an adsorbed layer at 0.289 nm above the topmost tetrahedral site, in agreement with the experimental value of 0.275 ( 0.01 nm obtained by Fenter et al. (8). A distinct second peak can also be seen as well as a third small peak. The water density fluctuations converge to bulk density at 1.0-1.2 nm away from the surface. We refer readers to a previous publication (7) for a detailed description of the orthoclase-water interface and extensive comparison with experimental data. Additionally, Figure 2 shows that the diffusivity of water molecules decreases as they approach the surface. The surface effects on the water diffusion become visible from 2.0 to 2.5 nm. Therefore, our simulations suggest that the orthoclase surface affects the dynamical properties of water beyond the point where the water density appears bulk-like. As a result of the long distances required to converge to bulk behavior, the selfdiffusion coefficient of water never reaches its bulk value for the smallest pore width (L ) 2.5 nm) and is calculated to peak at about 90% of the bulk value. For the middle-sized pore width (L ) 5.0 nm), the diffusion coefficient equals that of the bulk only within a small region in the center of the pore that has a width of less than 1.0 nm. Only the largest pore width (L ) 10.0 nm) shows a diffusion profile with a significant region within which the water mobility is that of bulk water. Figure 3 shows that the diffusion coefficient profiles in the directions normal and parallel to the surface exhibit different behaviors in the interfacial region, as seen previously for other mineral-water interfaces (4-6, 12). Indeed, the diffusion in the direction parallel to the surface shows a

monotonous increase with distance whereas, in the direction normal to the surface, features can be seen that correspond to maxima and minima in the water density profile. The diffusion coefficient decreases in the high density regions and increases in the low density regions. The layered structure of water at the interface in the direction normal to the surface indicates that there are energy barriers separating the different layers. In the regions that separate the water layers, only the water molecules with kinetic energy along the normal to the surface sufficient to overcome these energy barriers are sampled. As a result, the diffusion coefficient in the interlayer regions increases with respect to that within each layer. The small peak at about 0.1 nm above the surface is due to the few water molecules that exchange with potassium ions in the surface cavities; due to the small number of such exchanges and the fact that water molecules in the cavities are not diffusing these peaks are not deemed to be significant. The uncertainty in the diffusion coefficient at each height was calculated by determining the standard deviation of the mean when the simulation data were separated in five blocks and is shown in Supporting Information. The uncertainties were found to be small throughout the interfacial region and did not exceed (0.06 × 10-9 m2 · s-1. The model orthoclase surface is terminated by potassium and hydroxyl ions (Figure 1). Electrostatic forces between the surface ions and water molecules result in an adsorbed, first water layer whose density variations follow the arrangement of the surface ions (7). The templating effect is propagated to the second layer albeit with a weaker binding between water molecules in the first and second layers than that between the mineral surface and the adsorbed water molecules. As a result, the effect of the direct binding of water molecules to the orthoclase surface slowly diminishes with subsequent layers. This causes the water diffusivity to decrease as water molecules approach the surface since they experience an increasing binding strength. Given that eq 1 requires a linear dependence of the MSD on time (i.e., D is obtained when in the linear regime), one may ask whether the water molecules in the first few water layers, whose motion is constrained with respect to that in the bulk, can be considered as being in the linear regime. Therefore, we included in Supporting Information the MSD plots of water in the directions normal and parallel to the surface at five heights above the surface, which show that, except for the water diffusion in the first hydration layer in the direction normal to the surface, the linear regime is reached in each case. From these calculations, we wish to extract the average water self-diffusion coefficient along a mineral fracture, i.e., in the direction parallel to the surfaces, which will be referred to as the pore diffusion coefficient, Dp, hereafter. We obtained Dp from a single MSD plot that considered all water molecules in a particular simulation regardless of their height above the surface. To extrapolate the averaged diffusion coefficient to larger pore widths than those modeled, a bulk water region was added to the L ) 10.0 nm profile with bulk density and bulk diffusion by assuming that the local diffusion coefficient becomes constant when it is more than 5 nm from the mineral surface. The results are shown in Figure 4. For the smallest pore width considered (L ) 2.5 nm), Dp is approximately 60% of the bulk diffusion and about 80% for the L ) 5.0 nm simulation. The pore diffusion coefficient reaches 90% of the bulk diffusion coefficient for a pore width of 10 nm and 99% at 80 nm. Therefore, our simulations indicate that deviations from bulk diffusion coefficient become negligible when the pore width is larger than 100 nm, and become important for pore widths of less than 20nm. Such small pore widths are relevant to natural feldspar grains. Micronetworks are known to exist in natural feldspar samples (20, 21) and nanosized pores are likely to be abundant. For example, VOL. 43, NO. 3, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 4. Pore diffusion coefficient of water as a function of pore width extrapolated from the three simulated fractures. The water diffusion coefficient is given both as calculated (left y-axis) and normalized to its bulk value (right y-axis). The pore width is given in nm (bottom x-axis) and relative to the water molecular size (top x-axis), which was taken to be the position of the first peak in the oxygen-oxygen radial distribution function obtained from a MD simulation of bulk water. The 100, 99, and 90% bulk diffusion coefficient levels are also shown as discussed in the text.

FIGURE 5. Water diffusion coefficient as a function of distance for a range of ionic strengths (L ) 5.0 nm, uncharged surface). Dultz et al. (22) obtained pore size distributions for six feldspar samples using mercury intrusion porosimetry and found that maximum positions in these distributions varied from 20 to 540 nm. Fitz Gerald et al. (23) have also shown evidence of “nanotunnels” in alkali feldspars from scanning electron microscopy and transmission electron microscopy. To investigate the effect of ionic strength on the diffusion of water, we carried out a series of MD simulations where the orthoclase fracture was filled with a sodium chloride solution of concentration of 0.25, 0.50, or 1.00 mol · dm-3 for each of the three pore widths considered for the pure water simulations (the calculation of the 0.25 mol · dm-3 solution in the 2.5 nm pore width was not carried out as it resulted in a very small number of Na+ and Cl- ions). The water diffusion coefficient profiles obtained after 10 ns of dynamics are shown in Figure 5 for L ) 5.0 nm. The overall effect of the electrolyte ions is to slow down the water diffusion as has been shown previously for bulk solutions both experimentally (24-26) and theoretically (27, 28). Figure 5 shows that this effect is, within the uncertainty of our approach, independent of the distance from the surface. We also examined the effects of charged surfaces on the diffusion of water and the electrolyte ions. For the 5.0 nm pore width, we considered two surface charges (-7.2 and -14.4 µC · cm-2) for the case of a 0.50 mol · dm-3 sodium 780

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FIGURE 6. Water (top), sodium (middle), and chloride (bottom) diffusion coefficients as a function of distance for a range of surface charges (I ) 0.50 mol · dm-3 and L ) 5.0 nm). chloride solution. The surface charge was modeled by deprotonating 21 and 42% of surface silanol groups for the -7.2 and -14.4 µC · cm-2 surface charges, respectively. In both cases, the surface charge was compensated by adding sodium ions to the solution. Figure 6 shows that the effect on the water diffusion profile is small. At short distances from the surface, the diffusion coefficient decreases slightly with increasing surface charge due to the accumulation of sodium ions at the interface to compensate for the negative surface charge. As the number of electrolyte ions is constant, the increasing concentration of sodium ions at the interface implies a depletion at longer distances, which accounts for the slight increase of the diffusion coefficient in the middle of the pore. The sodium and chloride diffusion profiles are noisier since the number of sodium and chloride ions are much less than that of water. Longer simulated times will lead to better statistics and smoother profiles; however, the profiles shown in Figure 6 suggest that the effect of the surface charge on the electrolyte ion diffusion is also small at this high ionic strength. The uncertainties in the diffusion coefficients of the electrolyte ions were calculated at each height above the neutral surface as described above for water and are shown in Supporting Information. The uncertainties

diffusion coefficients in surface-charged clay porous media after accounting for the gradient of electrolyte concentration (29).

Acknowledgments

FIGURE 7. Water, sodium, and chloride diffusion coefficients (Di(r)) normalized to their respective bulk diffusion coefficients (Di(bulk)) as a function of distance (I ) 1.0 mol · dm-3, L ) 5.0 nm and uncharged surface). are larger than calculated for water with a maximum of approximately (0.2 × 10-9 m2 · s-1. The calculations were repeated for pure water where the only ions present in solution are the sodium ions required to compensate the surface charge (data not shown). Again, the water diffusion coefficient profile does not show a significant effect of the surface charge. Due to the small number of sodium ions in these simulations, large fluctuations are calculated for the sodium diffusion profile. Therefore, we cannot conclude whether the surface charge affects ion diffusion at low ionic strength and this issue will be addressed in future work. Finally, we ask whether the water and the electrolyte ions show a similar relative decrease in their diffusion coefficient as they approach the surface. To enable a reliable direct comparison of the relative diffusion coefficients, we extended the simulation of the 1.00 mol · dm-3 solution in the middlesized fracture to 25 ns. Figure 7 shows the water, sodium, and chloride diffusion profiles normalized to their respective bulk diffusion coefficient for L ) 5.0 nm. The electrolyte ions show convergence to bulk diffusion coefficient at the same distance away from the surface as water. However, from approximately 1.5 nm away from the surface, the sodium and chloride profiles diverge from that of water with the electrolyte ions being more noticeably slowed down (with relative diffusion coefficients of about 70-75% of that of water). In conclusion, our MD simulations indicate the presence of a 2.0-2.5 nm interfacial region within which the diffusivity of water and the electrolyte ions diminishes significantly. Extrapolation of the MD results to larger widths shows that this phenomenon will affect the diffusion in pores with widths up to several tens of nanometers. Therefore, in addition to factors that have been determined from macroscopic studies, the microscopic surface effects described in this work are an important component of the observed water diffusion decrease in the feldspar grain matrix. These effects stem from the electrostatic interactions between water and the mineral surface, which causes the water density to adopt a damped oscillatory profile. Such interfacial structures have been observed (3, 8) or calculated (4, 7) for a range of minerals. Therefore, we expect our conclusions to apply broadly to mineral-water interfaces. As observed in bulk solution, the presence of electrolyte ions reduces the water diffusivity but the calculations reveal that there is no significant distance dependence on this effect. Interestingly, we found that charged surfaces do not affect diffusion coefficients other than from the changes due to the redistribution of electrolyte ions at the interface. This result is consistent with measured

We acknowledge Dr. Eugene S. Ilton for useful discussions. This research was supported by the U.S. Department of Energy (DOE) through the Environmental Remediation Science Program (ERSP). The computer simulations were performed in part using the Molecular Science Computing Facility (MSCF) in the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL), a national scientific user facility sponsored by the U.S. DOE’s Office of Biological and Environmental Research (OBER) and located at Pacific Northwest National Laboratory (PNNL). PNNL is operated for the DOE by Battelle Memorial Institute under Contract DE-AC05-76RL01830.

Supporting Information Available Potential parameters and ionic charges. Water MSD plots at different heights. Uncertainties in water, sodium, and chloride diffusion coefficients.This material is available free of charge via the Internet at http://pubs.acs.org.

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