Ab Initio Determined Phase Diagram of Clean and Solvated Muscovite

Jan 7, 2016 - ABSTRACT: Focusing on muscovite mica, the most significant phyllosili- cate in the mica series, we determine its surface phase diagram ...
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Ab Initio Determined Phase Diagram of Clean and Solvated Muscovite Mica Surfaces Anoop Kishore Vatti, Mira Todorova,* and Jörg Neugebauer Department of Computational Materials Design, Max-Planck-Institut für Eisenforschung GmbH, Max-Planck Strasse 1, D-40237 Düsseldorf, Germany ABSTRACT: Focusing on muscovite mica, the most significant phyllosilicate in the mica series, we determine its surface phase diagram employing density functional theory. Surfaces in vacuum and in more realistic environmental conditions, that is, the surface in contact with water or an ionic liquid, are considered. These results naturally explain experimental observations such as the swelling of mica when it comes into contact with water.

mica’s widespread use as a substrate17−20 or explore the possibility to use it as a potential two-dimensional band gap engineering material.21 Initially, surfaces and interfaces of mica were studied by experiments, but in the last several years an increasing number of density functional theory (DFT) works have focused on mica surfaces, building on the experimentally available information. It has been suggested experimentally17 that cleaving muscovite mica disrupts only the potassium layer, while the structure of the aluminum-silicate layers remains undisturbed. Specifically, half a layer of K is expected to remain on the surface, although the potassium distribution is not necessarily uniform or ordered. As a consequence patches may form on the surface, which (locally) may not be charge compensated. This is corroborated by the observation that mica cleaved in UHV18 exhibits a higher surface potential compared to mica cleaved in air19 where the surface is easily contaminated and the local charge imbalance can be compensated by adsorbates. This observation, together with an experimental study suggesting a strong interfacial binding between graphene and mica surfaces stemming from van der Waals (vdW) interactions,22 have prompted Rudenko and co-workers20 to investigate the impact of surface charging and vdW-interactions on the adhesion of graphene on mica using a vdW-DFT approach. This study concludes that van der Waals interactions dominate the binding between graphene and mica at charge compensated mica surfaces, but are of secondary importance on charged surfaces. Sakuma15,16 uses DFT calculations to investigate changes in the adhesion energy between mica surfaces upon exchange of K+ ions by Na+ ions in the presence

I. INTRODUCTION Sheet silicates are among the most abundant rock-forming minerals in the Earth’s crust. Their base structure frame consists of sheets of tetrahedrally or octahedrally oxygen coordinated Si atoms, stacked in different sequences. In the probably most significant subgroup of such phyllosilicate minerals, the mica series, the layers consist of tetrahedral and octahedral sheets stacked in a 2:1 ratio to form a tetrahedral−octahedral− tetrahedral sheet (TOT) trilayer.1,2 These sequences of TOT trilayers are bonded by large intercalated cations,1,2 which ensure that any deviations from charge neutrality, due to substitutions within the Si-polyhedra are compensated. In muscovite mica the ions intercalated between subsequent TOT sheets are K+ ions. Muscovite mica is the most important representative of the mica series. It is easily cleaved into thin and sizable transparent sheets, resulting in its early use as window panes. The atomically smooth structure of such sheets, which are chemically inert, hydrophilic, and stable when exposed to electricity, light, moisture, and extreme temperatures, makes them very attractive for applications. Industrially, most sheet micas are used to make electronic devices.3,4 In scientific applications, muscovite mica is a commonly used substrate in various high-resolution atomic force microscopy (AFM)5 or surface force apparatus (SFA)6 measurements studying, for example, the structure of water7,8 or, in a biological context, the dynamics of enzymes.9 The abundance of phyllosilicates in the earth crust implies that they play an important role in seismic events, such as earthquakes or continuous fault slip. This has motivated a number of studies focusing on the elastic properties of bulk muscovite,10−14 but also some studies concerned with mica surfaces or interfaces to address their frictional behavior.15,16 Studies on muscovite mica surfaces or interfaces also arise from © 2016 American Chemical Society

Received: November 6, 2015 Revised: January 5, 2016 Published: January 7, 2016 1027

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Langmuir and absence of water. Based on DFT calculations, Alvim and Miranda23 simulated AFM images, X-ray adsorption spectroscopy (XAS), and solid-state nuclear magnetic resonance (SSNMR) spectra to identify characteristic features which would allow to distinguish a muscovite mica surface from surfaces of other sheet silicates with similar atomic arrangement. Finally, we mention the work of Kim et al.21 which presents a combined experimental/theoretical (DFT + U) study investigating the influence of layer thickness on the band gap of muscovite-type mica. Each of the mentioned works sheds light onto some aspect of mica surfaces and their interactions. However, a systematic investigation of possible surface structures, their thermodynamic stability, or the correlation between structure and local charge neutrality is still missing. We therefore combine in the present work first-principles calculations with thermodynamic concepts to investigate these aspects of muscovite mica surfaces. The focus will be on the (001) surface, which is the only observed surface orientation of muscovite mica and the surface that emerges when mica is cleaved. For this surface, we study the stability of several possible surface terminations and discuss the correlation between surface stability and local charge neutrality. An important aspect hereby is the thermodynamic stability of mica surfaces with respect to an excess or deficit of “K”-atoms for a wide range of environmental conditions using different exchange-correlation potentials.

cations, which renders the overall structure charge neutral. The K+ cations are intercalated between the trilayers and occupy gaps between the 12 oxygen atoms of the tetrahedral rings. The arrangement of Al and Si within the tetrahedral sheets in our structure is the site occupation found by Militzer and coworkers12 in their study on the lattice disorder of Al and Si sites within the tetrahedral and octahedral sheets of mica for their most favorable structure. This means that the smallest repeat unit in our bulk calculations is the (1 × 1 × 2) supercell containing 84 atoms, shown in Figure 1.

Figure 1. The bulk structure of muscovite mica is shown along the (010) direction (left) and the (100) direction (middle). The black box indicates the unit cell. (right) Supercell setup used for surface calculations showing two unit cells in the (001) direction. Atoms are shown as colored balls: hydrogen (white), oxygen (red), potassium (purple), silicon (blue), and aluminum (light blue). The coordination polyhedra around the silicon (dark blue polyhedra) and aluminum (light blue polyhedra) atoms are shown as well.

II. COMPUTATIONAL DETAILS We perform density functional theory calculations using the projectoraugmented wave method24 as implemented in the Vienna Ab initio Simulation Package (VASP)25 and both the semilocal Perdew− Burke−Ernzerhof generalized gradient approximation (PBE)26 and the hybrid PBE027,28 exchange-correlation (xc) functionals, with the standard Hartree−Fock mixing parameter of 0.25. The PBE0 calculations are also combined with an implicit solvation model (VASPsol29), to account for the influence of an environment other than vacuum. A plane-wave cutoff of 500 eV and a (4 × 2 × 1) Γ-point centered k-points mesh are used throughout the calculations. All surface structures were modeled in a supercell geometry using symmetric slabs of (001) orientation. A vacuum region of 25 Å ensures that consecutive slabs are decoupled. Careful convergence tests revealed that a slab containing a TOT trilayer is sufficient to obtain converged surface energies. Atoms within the central octahedral sheet (O layer/Al layer/O layer) were kept fixed to their bulk positions during relaxations, while all remaining atoms in the outer layers were fully relaxed. For geometry optimizations the conjugate gradient method was used and structures were relaxed until the residual forces on the atoms were less than 10−3 eV/ Å and an energy convergence of 10−8 eV was achieved for the final structure. Convergence tests show that these choices result in surface energies converged better than 10 meV/(1 × 1) unit cell. Variation of the implicit solvent thickness between 15 and 30 Å yield surface energies degenerate within the accuracy of our calculations.

In a recent study, we investigated the structural, electronic, and elastic properties of this bulk structure using several different functionals and comparing our findings to available experimental and theoretical information.31 Each of the tested functionals (two semilocal functionals (LDA,32 PBE26), a hybrid functional (PBE027,28), and a combination of PBE with the D2 dispersion correction by Grimme33 showed some deficiency in describing the studied structural, electronic, or elastic properties of muscovite mica. Based on these investigations, we decided to use in the present study both the PBE functional, which achieved a reasonable overall description of the structural parameters, and the PBE0 functional, which improves the description of the electronic structure, yielding a band gap within 1 eV of the measured one, when the standard Hartree−Fock mixing parameter α = 0.25 is used. Specifically, the PBE calculated band gap is 4.81 eV, the PBE0 one is 6.83 eV, and the measured band gap34 is 7.85 eV. Depending on the strength of the electronic screening of the material of interest, the standard value for the Hartree−Fock mixing parameter used in PBE0 may not always be the most appropriate choice and choosing α ∼ 1/ε typically improves the agreement between theory and experiment.35 Using our calculated electronic dielectric constant for muscovite mica, ε = 2.3, we find that α = 0.37, which complies with this rule, results in a band gap of 7.93 eV. The lattice parameters we calculate for muscovite mica using PBE are aPBE = 5.31 Å, bPBE = 9.11 Å, cPBE = 20.01 Å, and βPBE = 92.9°. The PBE0 lattice parameters, optimized using α = 0.25 and used for all PBE0 calculations reported in this work, are aPBE0 = 5.26 Å, bPBE0 = 9.13 Å, cPBE0 = 20.57 Å, and βPBE0 = 95.6°. Each of these values is within 3% of the reported experimental values10 (aEXP = 5.16 Å, bEXP = 8.95 Å, cEXP = 20.07 Å, and βEXP = 95.75°).

III. RESULTS AND DISCUSSION III.1. Bulk Muscovite Mica. The trilayer structure of the 2M1 muscovite mica KAl2(AlSi3O10) (OH)2 polytype is formed by an octahedral sheet, consisting of aluminum hydroxyoctahedra, sandwiched between two tetrahedral sheets build from SiO4-units.1,30 The SiO4 building blocks of a tetrahedral sheet are connected to each other forming quasi-hexagonal rings. Within some of the tetrahedral units Si4+ cations are replaced by Al3+, so that the SiO4 to AlO4 ratio within a tetrahedral sheet is 3:1. The negative charge induced in the tetrahedral sheet by the above replacement is balanced by K+ 1028

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Figure 2. Top view (upper panel) and side view (lower panel) of the studied (001) surface terminations. Shown are the (a) K-deficient surface termination, (b) a surface terminations in which K at the surface occupies the position within the Si5Al1 hexagonal ring, (c) a surface termination in which the surface K occupies the position within the Si4Al2 hexagonal ring, and (d) the K-excess surface termination. The surface unit cell is marked in the top view of each structure by a black rectangle.

Figure 3. Surface energy as a function of the K chemical potential for the studied (001) muscovite mica surface terminations obtained by (a) PBE and (b) PBE0 calculations.39 The surfaces have been embedded in vacuum and, in addition in panel (b), in water and an ionic liquid. The corresponding lines are marked by ε = 12.3 (ionic liquid) and ε = 80 (water). The range of thermodynamically allowed potassium chemical potentials in an aqueous environment are derived in panel (c). (c) Dependence of the K+, OH−, and H+ ions formation energy on the electron chemical potential. The formation energies are shown for several conditions representing the water stability region. To ensure thermodynamic stability the formation energies of the potassium ions must be positive (endothermic). Using this condition the boundaries of possible K chemical potentials can be determined and are shown in panels (a) and (b) by the light cyan shaded region bracketed by vertical black dashed lines. The light blue shaded regions highlight the water stability window at H-rich and O-rich conditions, respectively, while the two vertical black dashed lines encompass all the μe chemical potentials accessible within the electrochemical stability region of water. Ion formation energy lines important under H-rich conditions are shown as dashed blue lines. Ion formation energy lines important under O-rich conditions are shown as full blue lines. The two horizontal black dashed lines mark the formation energy values ΔfG defining the boundaries of the pH-scale.40 (d) Dependence of the concentration of K+-ions in water at standard conditions (1 M solution and T = 300 K) on the chemical potential of potassium μK. The relevant range is shown as a light blue area bracketed by two black lines. This range is determined using the intersection points between the K+-ions and their counterions OH− at the respective “H(O)-rich conditions” seen in (c). In all these figures, the reference zero value for μK is bulk potassium and for μe the vacuum level. 1029

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Table 1. Surface Energies Calculated for the Considered Surface Terminations of the Muscovite Mica (001) Surface in Contact with Vacuum, Water, or an Ionic Liquid (IL)a vacuum PBE Muscovite Muscovite Muscovite Muscovite a

no K (Figure 2a) 1K (Figure 2b) 1K (Figure 2c) 2K (Figure 2d)

115.10 14.98 13.57 10.75

water (ε = 80) PBE0

(1844.02) (240.01) (217.41) (172.23)

146.72 17.32 15.03 9.34

PBE0

(2350.70) (277.43) (240.82) (149.66)

142.69 0.49 −0.14 −11.55

(2286.14) (7.82) (−2.24) (−185.08)

IL (ε = 12.3) PBE0 145.68 6.38 5.25 3.30

(2333.99) (102.22) (84.25) (52.82)

The listed surface energy values are for potassium rich conditions (μK = 0) and given in meV/Å 2 (mJ/m2).

III.2. Structural Properties of the Muscovite (001) Surface. The (001) surface is the most relevant surface of muscovite mica and is formed when this mineral is cleaved. For the (001) surface the c-axis is normal to the surface. Four principal terminations of the (001) surface are possible: these are related to the presence (or absence) of potassium at the two high symmetry sites a potassium atom can occupy on the surface. The respective surface structures are shown in Figure 2. When K is present on the surface, it resides in the hollow sites within the hexagonal rings and is thus surrounded by six oxygen atoms. When there is only one K atom, it can occupy either the space within a Si5Al1 hexagonal ring (structure shown in Figure 2b) or the space within the Si4Al2 hexagonal ring (structure shown in Figure 2c). Our calculations show a preference for the second geometric arrangement (K residing within the Si4Al2 hexagonal ring, Figure 2c) which is 0.2 eV more stable than the configuration with the Si5Al1 ring. For the stable single potassium configuration (K in the Si4Al2 hexagonal ring, Figure 2c), the potassium atom relaxes toward the plane of the tetrahedral oxygen, so that the resulting K−O bond length is 2.89 Å (ΔdKO = −7.4% of the bulk bond length) when PBE is used and 2.88 Å (ΔdKO = −10.27%) with PBE0. The distance between the K plane and the nearest oxygen plane within PBE is 1.18 Å (ΔdKO = −35.79% of the bulk distance) and 0.98 Å (ΔdKO = −46.70%) when the hybrid PBE0 functional is used. The large reduction in bond length is indicative for a substantial increase in the bond strength. The origin is the loss in bonding coordination - the absence of the oxygen−potassium bond on the opposite site as in bulk reduces the total number of bonds which is partly compensated by the system in strengthening the individual bonds. III.3. Thermodynamic Stability of the Muscovite (001) Surface. The surface energy of the mica surface structures can be evaluated using the following equation:36,37 γ=

1 [Eslab − NME bulk − NK μK ] 2A

formation of K precipitates or droplets. Finally, A is the surface area of the slab and the 2 in the denominator accounts for the fact that the slab contains two equivalent surfaces. For stoichiometric surfaces, which do not contain an excess or deficit of potassium (structures (b) and (c) in Figure 2), the last term within the above equation becomes zero (since NK = 0) and the surface energy becomes a constant value independent of the chemical potential: γ=

1 [Eslab − NME bulk ] 2A

(2)

For the most stable stoichiometric structure (Figure 2c), the calculated surface energy is 13.57 meV/Å2 (0.217 J/m2) using PBE and 14.98 meV/Å 2 (0.240 J/m2) using PBE0. This is slightly higher than the range of surface energies of 9.36−12.48 meV/Å 2 (0.15−0.20J/m2) obtained by Christenson38 from surface force apparatus measurements. To evaluate the stability of nonstoichiometric surfaces, we show in Figure 3 the change of the surface energy with respect to a changing potassium chemical potential μK. Within these plots, the thermodynamically most stable surface termination at given conditions is the one with the lowest surface energy. For surfaces in contact with vacuum, Figure 3a and b shows the results for calculations performed with PBE and PBE0, respectively. To describe muscovite mica surfaces in contact with an aqueous electrolyte or an ionic liquid we also performed PBE0 calculations using an implicit solvation model.29 Such a model mimics the presence of an electrolyte by embedding the surface in a continuum dielectric medium that closely resembles the screening behavior of the environment/medium. The use of an implicit solvent model is somewhat limited, in that it is unable to account for explicit covalent bonds which might form between the water layer and the studied surfaces. Previous molecular dynamics (MD) studies by Sakuma and coworkers,15,41,42 in which both classical potentials and ab initio MD were used to study water at the mica(001) surface, indicate that the water-surface interactions are mainly Coulombic in nature. Because of these observations and our consideration of ideal (i.e., nondefective) mica surfaces, which are free of partially occupied reactive dangling bonds that could form covalent bonds with water molecules, the inability of the implicit water model to describe covalent bonds should not affect the results presented here, in particular also because the here used implicit solvation model describes the effect of electrostatics, cavitation, and dispersion on the interaction between the solute (mica) and the solvent by considering a spatially varying permittivity. This spatially varying permittivity depends on the solute charge density and emulates effects of the first solvation shell, for example, that the relative permittivity of the solvent close to the solute is lower compared to the equilibrium bulk value.29 The surface energies obtained

(1)

Here γ is the surface energy, Eslab is the calculated total energy of the symmetric slab, Ebulk is the calculated total energy of the bulk unit cell, and NM is the number of unit cells that are contained within the slab. NK is the number of K atoms which are in excess or deficiency compared to the stoichiometric surface termination, that is, the surface termination with only 1 K atom within the surface unit cell, since the two surfaces resulting from the cleavage have to share the two K atoms present in the bulk cell. The reservoir with which the potassium atoms are exchanged is represented by the K chemical potential μK, which is referenced with respect to bulk potassium, that is the energy a K atom has in a perfect bulk bcc K crystal. This choice of reference for the potassium chemical potential means that μK = 0 corresponds to “K” rich conditions. Going to higher K chemical potentials would make the surface unstable against 1030

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Langmuir for a water/mica (001) interface and an ionic liquid/mica (001) interface are shown in Figure 3b. The respective lines are marked by the respective screening constant ε of the used medium: ε = 80 for water and ε = 12.343 to model the commonly used ionic liquid [C2mim][Tf2N]. (The name of the ionic liquid [1-ethyl-3-methylimidazolium][bis(trifluoromethylsulfonyl)imide] is conventionally abbreviated as [C2mim][Tf2N].) For K-rich conditions, all the thus calculated surface energies are compiled in Table 1. Figures 3 a and b reveal that the sequence of stable structures does not change by the consideration of these different environments or the choice of exchange-correlation functional: a structure with two potassium atoms within the surface unit cell (Figure 2d) is most stable at K-rich conditions, a stoichiometric structure with one potassium atom within the unit cell (Figure 2c) becomes stable at intermediate μK conditions and the K deficient structure (Figure 2a) dominates at low μK values. The presence of an environment other than vacuum lowers the surface energy of each considered surface termination. The effect is, however, hardly visible for the rather smooth Kdeficient surface, for which the mica/vacuum, mica/ionic liquid and mica/water energies can be considered to be energetically degenerate. In contrast, for the more corrugated surfaces, in which the presence of the solvent screens the K+ ions at the surface the effect is strong and leads to a substantially reduced surface energy. The energy reduction achieved for the “Muscovite 1K” and the “Muscovite 2K” structure by the presence of water is rather similar, indicating that even in the denser “Muscovite 2K” structure the K+-ions are sufficiently separated, that is, the distance between neighboring K+-ions is large enough to allow the solvent molecules to enter, that is, to allow the dielectric medium to efficiently screen their repulsive electrostatic interactions. This is seen in Figure 4, which shows the induced charge of the mica surface screened by the solvent. A comparison of these two surfaces in contact with the ionic liquid reveals an incomplete screening of the K+ ions in the denser structure (“Muscovite 2K”), thus the calculated interface energy lies closer to the one calculated for the surface in vacuum. The rather pronounced asymmetry seen in the induced (screening) charges of the ’Muscovite 2K’ surface in contact with the ionic liquid is caused by a slight asymmetry in the distribution of the K+ ions on this surface (distances between K+ ions on the surface differ by ca. 0.2 Å). A further interesting aspect is that the energy for the most stable surface (“Muscovite 1K”) becomes zero/slightly negative when coming into contact with water (see red line for ε = 80 in Figure 3b). A negative interface energy implies a thermodynamic driving force that tries to maximize the interface area between the mica surface and water. This finding provides an intuitive explanation of the experimental observation that mica swells in the presence of water,44,45 since the negative interface energy provides a strong driving force for the penetration of water molecules into the muscovite structure. In contrast, the energies calculated for the mica/ionic liquid interface are positive, that is, there is no thermodynamic driving force to maximize the contact area between the surface and the ionic liquid. Indeed, the ionic liquid with ε = 12.3 we simulate here, [C2mim][Tf2N], is known not to induce swelling of mica.46 Finally, we note that in the range of potassium chemical potentials that can be realized in an aqueous environment (highlighted in Figure 3a and b by the light cyan shading) only stoichiometric surface structures (in our case the “Muscovite

Figure 4. Top view (upper panel) and side view (lower panel) of the distribution of the screening charges in the solvent at the stable “Muscovite 1K” (Figure 3c) and the “Muscovite 2K” surface structures embedded in implicit water or ionic liquid. Regions of electron depletion (positive charge density in the order of 10−5 e−/Bohr3) are shown in yellow and regions of electron accumulation (negative charge density in the order of −10−5 e−/Bohr3) are shown in blue. Note the quantitatively different screening of the dense “Muscovite 2K” structure with the ionic liquid (where the screening between the two K atoms is absent) and with water (where a pronounced screening occurs). The charge seen in the center of the slab (side view) is an artifact of the implementation of the implicit solvation model,51 but has not effect on the energetics.

1K” structure shown in Figure 2c) are thermodynamically stable. To connect the respective μK-values to concentrations of K+-ions in water, which are experimentally measurable and controllable, we employ our recently derived approach that extends semiconductor defect chemistry to electrochemistry.40 As input we use the formation energies of the respective ions in water. These are K+-ions and OH−-ions, which balance the concentration of K+-ions forming when the mica surface comes into contact with (chemically pure) water. The ion formation energies are calculated utilizing a Born cycle and tabulated energies47 rendering ΔfG(K+) = 2.206 [eV] − μK + μe and ΔfG(OH−) = −3.77 [eV]+ μH − μe.40 The resulting equilibrium K+ formation energies are shown in Figure 3c for various environmental conditions, represented by different values of the respective chemical potentials. K+ ions can exist in an aqueous solution only within the region of water stability. The boundaries for the variation of the chemical potentials, μK, μH and μe, are therefore determined by the electrochemical stability window of water. The electrochemical stability window of water can be obtained from the formation energies of hydrated H+ and OH− ions, as discussed in a recent publication.40 To determine the allowed range of chemical potentials we consider the ion formation energies ΔfG(H+) and ΔfG(OH−) for the two extreme conditions defining the water stability, that is, water in equilibrium with a H2 atmosphere (H-rich conditions) and water in equilibrium with an O2 atmosphere (O-rich conditions). The respective lines are shown in Figure 3c. These bounds determine the electron chemical potential conditions (μe values) at which these formation energies become negative, that is, μe at H(O)-rich for which ΔfG(OH−) = 0 and ΔfG(H+) = 0. Negative formation energies imply that 1031

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the formation of the ions becomes exothermic, that is, water is no longer stable but forms H2 and O2 molecules. The corresponding regions are highlighted in Figure 3c as light blue colored areas. Using this information allows us to directly determine the range of μK values consistent with the water stability region by identifying the thermodynamically allowed (ΔfG, μK, μe)-combinations53 for which the ΔfG(K+)-lines intersect the water stability region. The respective Δf G(K+) -lines are shown in Figure 3c. These can be used to evaluate the concentrations of K+-ions in water, cK+ = c0 exp(−ΔfG(K+)/ kBT), which is shown for standard conditions (T = 300 K and a 1 molar water solution, i.e. reference concentration c0 = 55.55 mol/L) in Figure 3d. For example, at H-rich conditions and μK = −3.684 eV we get cK+ = 55.55 mol/L × exp(−1.06 eV/ 0.02585 eV) = 8.7 × 10−17 mol/L and − log10(cK+/c0) = 17.8. The described approach can be used also to connect μK to the concentration of K+ ions in any ionic liquid, provided that the respective K solvation energy and stability range of the ionic liquid are known.

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IV. CONCLUSIONS In this work, we investigate the surface stability of different mica (001) surface terminations in contact with various environments. Comparison of the surface phase diagrams constructed using energies obtained from DFT calculations with the semilocal PBE and the hybrid PBE0 functionals show that the severe underestimation of the band gap by 3.04 eV (39% for PBE) has no impact on the sequence of stable structure within the surface phase diagram. However, it strongly affects the absolute values defining their respective stability range. Converting the potassium chemical potential into a K+ concentration scale reveals that only stoichiometric mica/water interface structures with incomplete K layers (a surface structure containing only half of the potassium ions found between two tetrahedral sheets in the bulk crystal) are relevant under realistic conditions. The slightly negative surface energy we find when the (001) surface is exposed to water explains the observed swelling of mica when it comes into contact with an aqueous electrolyte and the absence of swelling, if it is in contact with an ionic liquid such as [C2mim][Tf2N]. The approach and insights outlined in the present study are general and can be straightforwardly applied for other sheet silicates.

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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 Markus Valtiner for numerous discussions and critically reading the manuscript prior to submission. We thank Richard Henning and Kiran Mathew for helpful discussions regarding the implementation and use of the implicit solvation model VASPsol. Funding by the IMPRS-SurMat is gratefully acknowledged. The funding by the European Research Council under the EU’s seventh Framework Programme (FP7/2007− 2013)/ERC Grant Agreement 290998 is gratefully acknowledged. This work is supported by the Cluster of Excellence RESOLV (EXC 1069) funded by the Deutsche Forschungsgemeinschaft. 1032

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on Charging and Layering at Electrified Ionic-Liquid/Solid Interfaces. Adv. Mater. Interfaces 2015, 2, 1500159. (47) We consider the formation of the potassium ion starting from potassium bulk: cohesive energy of potassium (Ecoh (K) = 0.922 eV48) + ionisation energy of potassium (ΔIEG (K) = 4.34066 eV48) + hydration energy of a potassium ion (ΔhydG(K+) = − 3.057 eV49,50). (48) Lide, D. R. CRC Handbook of Chemistry and Physics, 86th ed.; CRC Press Inc.: Boca Raton FL, 2005. (49) Marcus, Y. The thermodynamics of solvation of ions. Part 2. The enthalpy of hydration at 298.15 K. J. Chem. Soc., Faraday Trans. 1 1987, 83, 339−349. (50) Marcus, Y. Thermodynamics of solvation of ions. Part 5. Gibbs free energy of hydration at 298.15 K. J. Chem. Soc., Faraday Trans. 1991, 87, 2995−2999. (51) The relatively big pores found within muscovite mica are apparently considered to be “vacuum” region within the current implementation and parametrization of VASPsol, for which reason some leaking of polarization charge into the center of the slab is observed. This charge leaking can be prevented by reducing the cutoff charge density parameter NC_K from its default value of 0.0025 to 0.002 Å. Applying this change modifies the surface energies marginally and has a negligible effect on the surface phase diagram shown in Figure 3b. For the actual calculations, we used the original rather than the modified parameter, since the default value of the NC_K parameter was not fitted independently from the other shape parameter SIGMA_K describing the width of the dielectric cavity.29,52 (52) Gunceler, D.; Letchworth-Weaver, K.; Sundararaman, R.; Schwarz, K. A.; Arias, T. A. The importance of nonlinear fluid response in joint density functional theory studies of battery systems. Modell. Simul. Mater. Sci. Eng. 2013, 21, 074005. (53) The boundaries defining the relevant concentration range in Figure 3e are determined from the (ΔfG, μK, μe) combinations: (0, −1.564, −3.77) and (1.06, −3.684, −4.83) for H-rich conditions; (0, −2.794, −5) and (1.06, −4.914, −6.06) for O-rich conditions. All values in eV.

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DOI: 10.1021/acs.langmuir.5b04087 Langmuir 2016, 32, 1027−1033