Viscosity of Nanoconfined Water between Hydroxyl Basal Surfaces of

Mar 6, 2013 - Kaolinite ([Si4]-Al4O10(OH)8)(1) is the most prevalent 1:1 type clay. .... (19) All simulations used a time step δt = 1 fs. ..... of Ai...
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Viscosity of Nanoconfined Water between Hydroxyl Basal Surfaces of Kaolinite: Classical Simulation Results Neil R. Haria,† Gary S. Grest,‡ and Christian D. Lorenz*,† †

Theory & Simulation of Condensed Matter Group, Department of Physics, King’s College London, London WC2R 2LS, United Kingdom ‡ Sandia National Laboratories, Albuquerque, New Mexico 87185, United States ABSTRACT: Whereas the structure of water near kaolinite surfaces is now fairly well understood, the dynamics of water confined between two kaolinite surfaces has not been studied. We conducted classical molecular dynamics simulations of nanoconfined water under shear between the hydroxyl basal planes of two kaolinite substrates to study the structural and dynamic properties of the nanoconfined water as a function of the amount of water in the system and the applied load. We found that the orientation of the water molecules within the first monolayer (∼3 Å) of the kaolinite interfaces changes as a function of load on the system. At low loads, the majority of the water molecules are oriented with one OH bond parallel to the kaolinite interface and the hydrogen atom of the other OH bond nearer to the kaolinite interface and a smaller population of water molecules are oriented with both hydrogen atoms further from the interface than the oxygen atom. At higher loads, while the same orientations are observed, another population of water molecules are oriented with one OH bond parallel to the interface and one OH bond in which the oxygen atom is nearest to the kaolinite interface is observed. The maximum value of viscosity observed is only 1 order of magnitude larger than the bulk shear viscosity at the same pressure.

I. INTRODUCTION Kaolinite ([Si4]-Al4O10(OH)8)1 is the most prevalent 1:1 type clay. It is found in soils, sediments, and atmospheric particles2−4 as part of clay particles that predominantly have diameters of the micrometer length scale and therefore have a large surface area. Within the soil, kaolinite plays a significant role in a variety of physicochemical processes including transport, distribution, and retention of dissolved species. Kaolinite has numerous applications in the chemical, medical, geological, and material industries.5 Contact between the kaolinite surface and an aqueous solution plays a significant role in these processes. Therefore, understanding water− kaolinite interfaces in microscopic detail is important. Kaolinite is a layered aluminosilicate material in which each layer contains one tetrahedral (silica) sheet and one octahedral (alumina) sheet held together by oxygen anions shared by the Si and Al atoms in the two sheets. The external surfaces of the alumina octahedra contain structural hydroxyl groups. Thus, individual kaolinite layers are held together by hydrogen bonds. This structure results in two different types of basal surfaces (hydroxyl and silica surfaces) and edge, or “broken”, surfaces containing numerous dangling bonds. Each surface interacts differently with water. Water adsorption and structure near kaolinite surfaces have been the focus of several publications, with the majority investigating the basal kaolinite planes.6−13 Using classical molecular dynamics (MD) simulations, Warne et al. found a significant degree of ordering of water near basal kaolinite interfaces. Near the hydroxyl surface, hydrogen bonding resulted in water molecules diffusing 40× slower than in bulk water.6 Tunega et al. used ab initio MD simulations of a single © 2013 American Chemical Society

water monolayer in contact with the two kaolinite basal planes and showed that the hydroxyl interface of kaolinite is hydrophilic owing to the amphoteric nature of the hydroxyl groups, whereas the silica interface is hydrophobic.7,8 They found that at the silica surface water molecules aggregate as they primarily form hydrogen bonds between themselves and only form weak hydrogen bonds with the surface.8 Solc et al. used classical simulations to study wetting by a droplet of water on each of the basal planes of kaolinite. They found complete spreading on the hydroxyl surface, while they observed a contact angle of 105° on the silica interface.13 Hu et al.9,10 carried out ab initio and Croteau et al.11,12 carried out classical grand canonical Monte Carlo simulations, respectively, to study ice nucleation at the basal surfaces of kaolinite. Hu et al. observed that the most stable monolayer of water molecules near the hydroxyl surface of kaolinite consists of 2/3 of a monolayer with the water molecules oriented such that half are parallel to it and half have their dangling OH bond directed toward the substrate, and this overlayer was found to have a stability similar to that of ice Ih.9,10 Croteau et al. also found that while there is increased hydrogen bonding at the hydroxyl surface and an increased density of water, they hypothesized that ice formation is not thermodynamically preferred and correspondingly rare at the basal surface due to the lattice mismatch between the surface and the structure of ice.11,12 Although the structure of adsorbed water molecules on the basal kaolinite surfaces has been studied thoroughly, the Received: December 11, 2012 Revised: February 13, 2013 Published: March 6, 2013 6096

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Figure 1. Snapshots of the simulated systems containing (a) 17, (b) 26, and (c) 43 water molecules/nm2 confined between two kaolinite substrates. The different atomic species are represented by different colors: oxygen atoms are red, hydrogen atoms are white, aluminum atoms are silver, and silicon atoms are yellow.

motion, while in the compression and shear simulations the thermostat was applied only in the vorticity direction (xdimension) so that its effect has a minimal effect on the dynamics of the system.19 All simulations used a time step δt = 1 fs. For the shear and compression simulations, we freeze the outermost layers of silicon and oxygen atoms in the kaolinite substrates and then use them to apply the necessary velocities to the two substrates. Each of the three systems was compressed in order to apply different loads. The compression simulations were conducted by applying a velocity of 0.5 and −0.5 m/s in the z-dimension to the frozen atoms in the bottom and top substrates, respectively. Then, we chose three different configurations from the resulting trajectories of the compression simulations and equilibrate at constant separation. The shear simulations are conducted applying a velocity in the y-direction of vy to the top substrate and −vy to the lower substrate, while holding the two substrates at constant separation. The shear properties of the confined water molecules were studied at three different velocities: vy = 1, 10, and 100 m/s. The shear simulations for vy = 100 m/s were run for 20 ns, while for the other two shear velocities, the simulations were ran for ∼80 ns. After the system reached steady state, we measured the friction force and applied load. Since the simulations were carried out at constant separation, the measured load under shear increased compared to its value at zero shear. We also conducted simulations of shear in the x-direction, which is the same direction as studied recently using ab initio molecular dynamics simulations.14 In this case, we applied a velocity of vx = 100 m/s to the top substrate and −100 m/s to the bottom substrate. The results of systems sheared in the xdimension were nearly identical to those measured for shear in the y-direction. While the bulk viscosity of SPC water has been determined at a pressure of 1 atm previously,20−22 it has not been reported for the high pressures studied here. To separate the effect of confinement on the viscosity of water from the simple increase in the bulk shear viscosity of water with increasing pressure, we carried out simulations to measure the bulk viscosity ηbulk versus pressure. We conducted simulations using the SLLOD algorithm23 of a system of 512 SPC water molecules at pressures ranging from 0.1 to 717 MPa for a range of shear rates from 1010.25 to 1011 s−1. From these results, we determined the zero shear rate viscosity ηbulk, which is plotted in Figure 2.

dynamics of water confined between kaolinite surfaces has not. Here we present the results of a series of classical MD simulations of nanoconfined water under shear between two kaolinite hydroxyl interfaces. We have studied the viscosity of the nanoconfined water as a function of amount of confined water and the applied load to the system. The results show that the viscosity of the water is increased by a maximum of an order of magnitude over the bulk shear viscosity in these systems. In parallel to our work, ab initio MD simulations have been used to conduct a similar study to that reported here.14 In his work, Feibelman also found that the maximum increase in the viscosity in his systems was an order of magnitude. In the remaining sections of the article, we first introduce our simulations and then present the results for the structural and dynamic properties of the confined water. Finally, we provide a comparison of our results with previous simulation studies.

II. MODEL AND METHODOLOGY We conducted classical MD simulations using the LAMMPS simulation package.15 Three different amounts of water confined between two kaolinite substrates: 17 (758 water molecules), 26 (1137 water molecules), and 43 (1895 water molecules) water molecules/nm2 (as depicted in Figure 1) were studied three different loads. Each kaolinite substrate is represented by a periodically repeated unit cell of dimensions 61.842 Å × 71.535 Å × 5.5 Å (Lx × Ly × Lz). They are oriented so that the hydroxyl basal plane of each substrate is in contact with the confined water. The surface areas of the substrates are 4 times larger than those described by Cygan et al.16 and obtained by replicating their system in the xy-plane. All nonbonded, bonded, and angle interactions in these systems were modeled using the CLAYFF force field,16 which was developed specifically for simulations of hydrated mineral systems and their interfaces with aqueous solutions. All hydrogen containing bonds and angles were constrained using the SHAKE algorithm.17 The CLAYFF force field uses the SPC three-point model for water. Bonds length and angles in water were also constrained using the SHAKE algorithm. The van der Waals interactions were cut off at 12 Å, and the long-range electrostatic interactions were calculated using the particle−particle particle−mesh (PPPM) algorithm.18 The temperature is maintained at T = 300 K by coupling the atoms to a Langevin thermostat. During the equilibration simulations, the thermostat is coupled to all three directions of 6097

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The average orientation of the water molecules as a function of distance normal to the interface (z-coordinate) can easily be determined by measuring the angle between the vector connecting the oxygen atom of the water molecule and the midpoint of the vector connecting the two hydrogen atoms of the water molecule and the ⟨0,0,1⟩ vector as shown in Figure 4a. The orientation angle θ is defined such that when the zcoordinate of the oxygen atom of the water molecule is larger than the z-coordinate of the center point between the two hydrogen atoms, θ < 90°; when the z-coordinate of the center point between the two hydrogen atoms is larger than the zcoordinate of the oxygen atom, θ > 90°; and when the two points have equal z-coordinates, then θ = 90°. The average orientation angle as a function of the z-coordinate for the three different thicknesses of water layers at high loads is shown in Figure 4b. In each case, near the kaolinite surfaces the water molecules lie such that the vector connecting the oxygen atom of the water molecules and the center point of the hydrogen atoms makes an angle of ∼45° with the kaolinite substrate. Thus, the midpoint of the two hydrogen atoms is nearer to the kaolinite substrate than the oxygen atom. For water molecules farther from the interface, the average orientation approaches 90°, corresponding to a random orientation of the water molecules. This behavior does not depend on load or shear velocity, so plots of these dependences are not shown. We have also investigated the orientations of water molecules within 1 Å thick layers away from the kaolinite substrate. The layers were defined by calculating the minimum distance in the z-coordinate between the oxygen of a given water molecule and an atom in the kaolinite substrate. For molecules in the 43 water molecules/nm2 system at a load of 190 MPa, Figure 5 displays the percentage of water molecules within the different layers tilted at angles (θ1, θ2) from the ⟨0,0,1⟩ vector. If θ1 or θ2 is greater than 90°, then the OH bond is oriented such that the hydrogen atom is farther from the kaolinite substrate. Alternatively, if θ1 or θ2 is less than 90°, then the oxygen atom is farther away. Figure 5 shows that most of the water molecules within 1 Å of the substrate are oriented such that both their hydrogen atoms are farther away from the kaolinite surface than the oxygen atom (θ1 > 90°, θ2 > 90°). Water molecules 1−3 Å removed from the kaolinite interface are oriented such that the majority have one OH bond approximately parallel to the kaolinite interface and the other oriented so that the hydrogen is nearest to the kaolinite (θ < 90°). These three layers are all within the first peak in the density observed in Figure 3 and therefore are part of the first monolayer. The layer of water molecules farthest from the substrate shows no preferred orientation, as the orientations are fairly evenly distributed. Similar distributions were observed at low loads for the 17 and 26 water molecules/nm2 systems. However, at higher loads, we observed a difference in orientation of the OH bonds of the water molecules within 2 Å of the kaolinite interface. Figure 6 show the percentages of water molecules that have a given pair of orientations of its OH bonds in relation to the z-axis. Note that most of the water molecules within 1 Å of the substrate are oriented so that one OH bond is parallel to the kaolinite interface (θi = 90°) and the other pointed away from the kaolinite substrate (θj > 150°). The water molecules in the next 1 Å thick layer are oriented such that the hydrogen atoms of both OH bonds are farther from the kaolinite surface than the oxygen atoms (θ1 > 90°, θ2 > 90°). Then, the water molecules that are 2−3 Å removed from the kaolinite surface are oriented

Figure 2. Zero shear rate viscosity ηbulk as a function of pressure.

Our result, for the SPC model at ambient pressure, is 0.41 cP. That is slightly larger than previous estimates,20−22 though we used a larger cutoff of 12 Å for the van der Waals interactions than these previous studies. This value is small compared with an experimental value of 1.0 cP but consistent with previous findings20−22 that the SPC model underestimates the shear viscosity of bulk water. The results shown in Figure 2 are used to normalize the measured viscosity of the confined systems.

III. STRUCTURAL PROPERTIES OF CONFINED WATER The density profiles of the three different confined water systems for applied loads ranging from ∼270 to ∼720 MPa are shown in Figure 3. For each system there is a peak in the water

Figure 3. Density of kaolinite (black circles) and water (blue squares) in the 17 (a−c), 26 (d−f), and 43 (g−i) water molecules/nm2 as the applied load increases. The specific applied load in each system is (a) 270, (b) 470, (c) 530, (d) 340, (e) 500, (f) 720, (g) 280, (h) 420, and (i) 590 MPa.

density at each kaolinite interface. For the 17 water molecules/ nm2 system, only two peaks are observed near the kaolinite interface, demonstrating that the system contains two monolayers. For the 26 water molecules/nm2 system, an additional region of water between the two interfacial layers of water molecules is observed. Lastly, two additional smaller peaks and another region between these two smaller peaks are observed for the 43 water molecules/nm2 system. The two peaks indicate two layers of water adsorbed to each kaolinite substrate. The additional region is a layer of unordered water molecules. 6098

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Figure 4. (a) Definition of the orientation angle, θ. (b) Average orientation angle as a function of the z-coordinate for the following systems: (i) 17 water molecules/nm2, load = 530 MPa; (ii) 26 water molecules/nm2, load = 500 MPa; and (iii) 43 water molecules/nm2, load = 590 MPa.

Figure 5. Percentage of water molecules in 43 water molecules/nm2 system (load = 190 MPa) that has an orientation such that one OH bond makes an angle θ1 with the ⟨0,0,1⟩ axis and the other OH bond makes the angle θ2 within 1 Å layers that are (a) 0−1, (b) 1−2, (c) 2−3, and (d) 3−4 Å from the kaolinite interface. The color scale is such that white is equal to 0%, blue is 1%, green is 2%, and red is 3% of the water molecules within a given layer.

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Figure 6. Percentage of water molecules in 43 water molecules/nm2 system (load = 460 MPa) that has an orientation such that one OH bond makes an angle θ1 with the z-axis and the other OH bond makes the angle θ2 within 1 Å layers that are (a) 0−1, (b) 1−2, (c) 2−3, and (d) 3−4 Å from the kaolinite interface. The color scale is such that white is equal to 0%, blue is 1%, green is 2%, and red is 3% of the water molecules within a given layer.

various studies25−27 to be appropriate, then friction force can be defined as a linear function of the normal pressure

such that the majority have one OH bond approximately parallel to the kaolinite interface. The other OH bond is oriented so that the hydrogen is nearest to the kaolinite interface (θ < 90°). The layer furthest from the substrate shows no preferred orientation, as the orientations are fairly evenly distributed.

F = τ0A + μAL

The experimentally measured or “macroscopic” coefficient of friction encompasses a number of phenomena (i.e., microscopic roughness) that we do not treat in our parallel slab simulations. Values of μ from our shear simulations of water confined between kaolinite substrates are shown in Table 1. As the shear velocity is increased, computed friction forces (Figure 7) and values of μ also increase. For our lowest shear velocity, 2 m/s, the values of the friction forces and the values of μ are too small to determine accurately. That is, their magnitudes are comparable to the estimated statistical error. We observed similar behavior in previous studies of water confined between hydrophilic self-assembled monolayers (SAMs)28 and amorphous silica substrates.29 As the amount of water confined between the two kaolinite substrates increases, we observe that the values of the friction forces and the values of μ decrease. These same trends were observed in our previous study of confined water between hydrophilic SAMs28 and in the experimental study of Qian et al.30

IV. DYNAMIC PROPERTIES OF CONFINED WATER A. Frictional Response. The steady-state friction force computed as a function of the applied load for the three different confined water systems and relative velocities of 2, 20, and 200 m/s is shown in Figure 7. The friction force and applied load were determined after reaching steady state by averaging these values over 10 ns for the 200 m/s shear and ∼70 ns for the two slower cases. Bowden and Tabor showed that the frictional force F is proportional to the contact area A24 F = τA

(2)

(1)

where the proportionality constant is the interfacial shear strength, τ. Assuming a first-order dependence of the shear strength on the load, L (τ = τ0 + μL), which has been shown in 6100

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Figure 7. Measured friction force as a function of applied load for the systems containing (a) 17, (b) 26, and (c) 43 water molecules/nm2. The different relative shear velocities are represented by different colors and shapes: 2 m/s (black circles), 20 m/s (red squares), and 200 m/s (blue ×’s).

Table 1. Values of the “Microscopic” Coefficient of Friction, μ, for the Three Different Confined Water Systems between the Kaolinite Substrates When Sheared at the Relative Shear Velocity of 20 and 200 m/s rel shear velocity (m/s)

17 H2O/nm2

26 H2O/nm2

43 H2O/nm2

20 200

0.08 0.10

0.05 0.05

0.03 0.04

molecules near the kaolinite substrate. The degree of slip decreases as the amount of water confined between the two kaolinite substrates increases. The magnitude of the average velocity of the water continues to decrease farther away from the kaolinite substrate, in a near linear fashion. At the midpoint between the two substrates, note that the magnitude of the average velocity of the water is zero. This velocity profile is in good agreement with that of Couette-like flow. From these velocity profiles, the shear rate of each system was calculated by determining the difference in the velocities at the top and bottom kaolinite interface and dividing it by the distance between the two interfaces. The calculated shear rates are approximately 2.5 × 109, 2.5 × 1010, and 2.5 × 1011 s−1 for the systems sheared at 2, 20, and 200 m/s, respectively. C. Viscosity of Confined Water. Besides the friction forces and the coefficients of friction reported above, we have also estimated the viscosity of the confined water. We used the same method to determine the viscosity of the water here as we have used previously,28 dividing the calculated shear stress by the shear rate obtained from the velocity profiles. The viscosity has been determined for the systems that have a relative shear velocity of 20 m/s (shear rate of ∼2.5 × 1010 s−1) and 200 m/s (shear rate of ∼2.5 × 1011 s−1). The shear rate determined for the 20 m/s systems is in the region in which the viscosity of bulk water has been observed to be independent of shear rate both in the bulk simulations for SPC water conducted for this paper and previously in the determination of the bulk viscosity of the TIP3P water.28 Figure 9 shows the relative viscosity η/ηbulk as a function of the applied load for the three confined water systems, where ηbulk is the viscosity of bulk SPC water at the applied load at

Although the equilibrium structures of the water near the kaolinite interfaces were different at small and large loads (see Figures 5 and 6), the orientation of the water molecules near the interface are similar at all loads under shear. The distribution of the orientation of the OH bonds in the water molecules near the kaolinite interfaces under shear are all similar to that observed at high loads in equilibrium. At least for the shear rates accessible in simulations, the shear dominates the effect of the load on the structure of the first few layers of water molecules. B. Velocity Profile within Confined Water during Shear. We also investigated the velocity of the water molecules in the shear direction as a function of location within the film. Figure 8 shows the velocity profiles of the three different confined water systems at the various loads studied when they are sheared at 200 m/s. Profiles are not shown for systems sheared at 20 and 2 m/s because they are similar. In each profile, notice that the water molecules within 3 Å of the kaolinite substrates move at nearly the same velocity as they are dragged along with the substrate. The density plots shown in Figure 3 display interfacial peaks in the density of water ∼3 Å in width, which suggests that the adsorbed monolayers are that size. Some slip occurs at the water/kaolinite interface. It can be seen as the difference between the velocity of the substrate and the first few data points of the velocity profile of the water 6101

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Figure 8. Velocity profiles of water molecules (blue squares) and kaolinite substrates (black circles) as a function of its position in the z-dimension for the systems under a relative shear of 200 m/s. The different plots are for systems containing (a) 17, (b) 26, and (c) 43 water molecules/nm2. The values of the velocity have been normalized by vy = 100 m/s.

Figure 9. Relative viscosity as a function of load for systems containing (a) 17, (b) 26, and (c) 43 water molecules/nm2. The two different plots represent the relative shear velocity of 20 m/s (red circles) and 200 m/s (blue squares).

for the systems containing 17, 26, and 43 water molecules/nm2, respectively. For the relative shear velocity of 200 m/s, the maximum measured viscosity is 3.5×, 2.4×, and 2× the bulk viscosity for the systems containing 17, 26, and 43, water

zero shear. As the amount of confined water increases, we observe that the measured viscosity decreases. For the systems sheared with a relative shear velocity of 20 m/s, the viscosity increased by approximately 15×, 8×, and 5× the bulk viscosity 6102

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molecules/nm2, respectively. Therefore, at 200 m/s, the water molecules in all of the systems show significant shear thinning, as was also observed for water confined between silica interfaces.29

The frictional response of the water confined between the two kaolinite interfaces demonstrates that the coefficient of friction decreases with increasing amounts of water within the system. This same trend has been observed in previous simulations of water confined between self-assembled monolayers.28 Also, the coefficient of friction that we have estimated increases with shear velocities, which has also been observed for water confined between amorphous silica substrates.29 The viscosity of the nanoconfined water decreases as the amount of water in the system increases. Also, the viscosities of the confined water decrease as the shear velocities increase also observed in the case of water confined between amorphous silica.29 When comparing the amount of increase in viscosity of the confined water in the two monolayer system (17 water molecules/nm2) between kaolinite and between amorphous silica, we find that the increase in viscosity is ∼6× larger in the kaolinite systems. While an increase of viscosity of the nanoconfined water is observed, the magnitude of this increase is at most 15× larger than the bulk shear viscosity. We do not observe an increase indicative of the formation of an ice layer on the kaolinite interface, which is in agreement with previous classical simulations.11

V. DISCUSSION We used classical molecular dynamics simulations to study the structural and dynamic properties of three different systems containing 17, 26, and 43 water molecules/nm2 confined between the hydroxyl interface of two kaolinite substrates. We investigated the density and orientation of the confined water molecules for a range of applied loads. We also studied the frictional properties of the confined water when shear is applied to the systems and the viscosity of the confined water during this shear. Our results show that the water molecules near each interface forms organized layers in agreement with previous classical simulations of the adsorption of water onto the hydroxyl surface of kaolinite.6,11−13 The water molecules nearest the kaolinite interface are oriented such that the oxygen of the water molecule is nearer to the kaolinite interface than the center of the two hydrogen atoms. This general trend holds independent of confining channel width and load. We found that the equilibrium distribution of the orientation of the individual OH bonds on a given water molecule depends on the applied load. At low loads, water molecules within 1 Å of the kaolinite interface are oriented with both hydrogen atoms further from the kaolinite interface than the oxygen. The water molecules in the next 2 Å, which make up the first density peak nearest the interface, are oriented with one OH bond parallel to the kaolinite interface and the hydrogen atom of one OH bond nearer to the kaolinite than the oxygen. This general distribution of orientations is similar to the orientations seen by Hu et al.9,10 and by Feibelman.14 They reported that the most stable structure of the water overlayer adsorbed to the hydroxyl interface has half of the water molecules oriented with one OH bond pointing toward the kaolinite and the other OH bond oriented parallel to the interface; the other half of the water molecules are oriented such that both of the OH bonds are parallel to the interface. At higher loads, the distribution of the OH bond orientations of the water molecules within the 2 Å of the kaolinite interface is noticeably different. The water molecules within 1 Å of the kaolinite interface are oriented with one OH bond parallel to the interface and one OH bond in which the oxygen is nearest to the kaolinite interface. Water molecules in the next layer are orientated such that both hydrogen atoms are further away from the kaolinite interface than the oxygen. In the third 1 Å thick layer, the water molecules are primarily oriented such that they have one OH bond that is parallel to the kaolinite interface and one OH bond which has its hydrogen atom nearer to the kaolinite interface than the oxygen. Thus the load has some effect on the orientation of water molecules nearest to the kaolinite interface. When the systems are sheared, the distribution of the OH bond orientations of the water molecules within 3 Å of the kaolinite interface is the same at all loads. The distribution is very similar to that measured at high loads in zero shear. Therefore, it appears that at least for the shear rates accessible in our simulations the effect of shear is dominant in determining the structure of the water near the kaolinite interfaces.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Randall Cygan and Peter J. Feibelman for helpful discussions. N.R.H. and C.D.L. acknowledge the support of the EPSRC (in the form of a DTA studentship) and King’s College London start-up funds for providing financial support of this project. This work is supported by the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy National Nuclear Security Administration under Contract DE-AC04-94AL85000.

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REFERENCES

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dx.doi.org/10.1021/jp312181u | J. Phys. Chem. C 2013, 117, 6096−6104