Monovalent Ion Adsorption at the Muscovite - ACS Publications

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Monovalent Ion Adsorption at the Muscovite (001)−Solution Interface: Relationships among Ion Coverage and Speciation, Interfacial Water Structure, and Substrate Relaxation Sang Soo Lee,*,† Paul Fenter,† Kathryn L. Nagy,‡ and Neil C. Sturchio‡ †

Chemical Sciences and Engineering Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, United States ‡ Department of Earth and Environmental Sciences, 845 West Taylor Street MC-186, University of Illinois at Chicago, Chicago, Illinois 60607, United States S Supporting Information *

ABSTRACT: The interfacial structure between the muscovite (001) surface and aqueous solutions containing monovalent cations (3 × 10−3 m Li+, Na+, H3O+, K+, Rb+, or Cs+, or 3 × 10−2 m Li+ or Na+) was measured using in situ specular X-ray reflectivity. The element-specific distribution of Rb+ was also obtained with resonant anomalous X-ray reflectivity. The results demonstrate complex interdependencies among adsorbed cation coverage and speciation, interfacial hydration structure, and muscovite surface relaxation. Electron-density profiles of the solution near the surface varied systematically and distinctly with each adsorbed cation. Observations include a broad profile for H3O+, a more structured profile for Li+ and Na+, and increasing electron density near the surface because of the inner-sphere adsorption of K+, Rb+, and Cs+ at 1.91 ± 0.12, 1.97 ± 0.01, and 2.26 ± 0.01 Å, respectively. Estimated inner-sphere coverages increased from ∼0.6 to 0.78 ± 0.01 to ∼0.9 per unit cell area with decreasing cation hydration strength for K+, Rb+, and Cs+, respectively. Between 7 and 12% of the Rb+ coverage occurred as an outer-sphere species. Systematic trends in the vertical displacement of the muscovite lattice were observed within ∼40 Å of the surface. These include a 99.9%, Sigma-Aldrich) in DIW (Table 1). The concentration of K+, Rb+, and Cs+ was 3 × 10−3 m (molal), a concentration sufficient to yield a cation coverage that nearly satisfies the negative charge of the muscovite surface.47 Solutions of Li+ and Na+ were prepared at both 3 × 10−3 and 3 × 10−2 m, with the higher concentration used because these cations are reported to have a lower adsorption affinity for the surface.15 A pH 2.5 HCl solution was prepared by diluting a high-purity 0.1 N HCl stock solution with DIW. The competitive adsorption of cations (e.g., Al3+) derived from muscovite dissolution is expected to be negligible on the basis of measured dissolution rates of muscovite at acidic pH and the time required to perform the experiments.48 Each crystal reacted with solution for more than 2 h before being transferred to a thin-film sample cell,49 where it was held in place by a Kapton membrane and remained in contact with the solution for the duration of the X-ray measurement. 2.2. X-ray Reflectivity Measurements. X-ray experiments were conducted at beamlines 6-ID-B (MU-CAT) and 33-ID-D (UNIXOR), Advanced Photon Source (APS) (previous studies23,49−51 and Supporting Information (SI)). Nonresonant XR was measured as a function of momentum transfer q (= 2πL/d, where L is the Bragg index of the muscovite (001) reflections and d = ∼19.96 Å20 is the (001) layer spacing) at a fixed photon energy (E). Each XR data set was obtained in less than 1 h. The stability of the experimental system was monitored by periodically measuring the reflectivity at two reference q values (= 0.85 and 1.83 Å−1). The measured X-ray reflectivity data, R(q) (Figure S1), are shown after being normalized to the generic crystal truncation rod (CTR) form factor, 1/[q sin(qd/ 4)]2,52 to enhance the visibility of the changes in the reflectivity signals (Figure 1). The resonant anomalous X-ray reflectivity (RAXR) of muscovite in a 3 × 10−3 m RbCl solution was measured by scanning the incident photon energy, E, around the X-ray K-edge absorption energy (Eo) of Rb at a series of q values (Figure 2). A complete set of RAXR

Table 1. Solution Compositions and X-ray Reflectivity Measurements solution composition

sample mu3Li mu30Li mu3Na mu30Na mu3H3O mu3K mu3Rb mu3Cs

3 30 3 30 3 3 3 3

× × × × × × × ×

−3

10 m LiCl 10−3 m LiCl 10−3 m NaCl 10−3 m NaCl 10−3 m HCl 10−3 m KCl 10−3 m RbCl 10−3 m CsCl

pHa

types of X-ray measurementsb

beamlinec

5.7 5.7 5.7 5.7 2.5 5.7 5.7 5.7

XR XR XR XR XR XR XR, RAXR XR

6ID-B 6ID-B 33ID-D 33ID-D 33ID-D 6ID-B 33ID-D 6ID-B

a Equilibrated with atmospheric CO2. bXR: (nonresonant) X-ray reflectivity. RAXR: resonant anomalous X-ray reflectivity. cLocated at the Advanced Photon Source at Argonne National Laboratory.

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Figure 2. RAXR spectra of muscovite (001) in a 3 × 10−3 m RbCl solution (mu3Rb) measured near the Rb K X-ray absorption edge (Eo). The spectra are normalized on the basis of the resonant amplitude normalization method,39 (|Ftot(q, E)|2 − |FNR(q)|2)/(2| FNR(q)|), where Ftot and FNR are the total and nonresonant structure factors, respectively. Each spectrum is labeled with the q value (Å−1) where the spectrum was measured and offset vertically by 4 for easier visual comparison. The solid lines through data points are calculated intensities derived from the best-fit models. Dashed gray horizontal lines indicate the theoretical normalized reflectivity when there is no resonant atom at the interface. species, and the water above the interfacial region.5,20,38,39,44−46 The reflectivity calculated from the model is expressed as

Figure 1. Normalized X-ray reflectivity at the muscovite (001)− solution interface. The X-ray reflectivity (R) is normalized by the generic crystal truncation rod intensity (1/[qsin(qd/4)]2, where q is the momentum transfer and d is the muscovite (001) spacing, ∼19.96 Å). Refer to Table 1 for the meaning of the sample labels. The solid black curves through the data points indicate the calculated reflectivity from the best-fit model for each set of data (Table 2). The calculated reflectivity from the best-fit model for muDIW (dashed cyan curves)55 is also shown for comparison. Each plot is offset vertically for visual comparison, as indicated below each sample label.

⎛ 4πre ⎞2 R(q) ∝ ⎜ ⎟ |FUCFCTR + FInt + FW |2 ⎝ qAUC ⎠

(1)

where re is the classical electron radius (= 2.818 × 10−5 Å), AUC is the unit cell area of the muscovite (001) surface (= 46.72 Å2),20 and FCTR is the structure factor for a semi-infinite crystal along the surface normal direction (= 1/[1 − exp(−iqd/2)]).49,52 The structure factors for a single unit cell of muscovite, the interfacial region, and bulk water (FUC, Fint, and FW, respectively) are calculated from

measurements required about 2 h. The stability of the experimental system was monitored by periodically measuring RAXR at q = 0.38 Å−1. The magnitude of the RAXR modulation increased systematically at the reference q by about 20% after about 1 h of exposure to the Xray beam. This indicates that long-time beam exposure altered the Rb distribution at the interface (SI text). To minimize the impact of this effect, we exchanged the solution in the sample cell and translated the sample perpendicularly to the beam direction to illuminate a fresh area of the surface with the X-ray beam whenever we observed a change in magnitude larger than ∼5% in any reference RAXR spectrum. The retrieval of the intrinsic interfacial structure was confirmed by the reproducibility of the RAXR spectrum at the reference q, after which the measurements were restarted. In this way, the full set of RAXR data covering a wide range of q (0.22−3.02 Å−1) was obtained with little or no artifacts related to beam−sample interactions. 2.3. Data Analysis. Nonresonant XR data were fit using a model consisting of the muscovite substrate lattice,20 the interfacial region including the relaxed muscovite surface and the adsorbed solution

⎡ (qu )2 ⎤ j ⎥ F = Σjcjf j (q) exp(iqzj) exp⎢ − ⎢⎣ 2 ⎥⎦

(2)

using the atomic scattering factor ( f j(q)), occupancy (cj), height (zj), and root-mean-square (rms) distribution width (uj) of the jth atom. The q-dependent variation of f j was calculated using coefficients from the International Tables for Crystallography.53 The atoms in the top two unit cells (including four 2:1 layers, each of which is composed of two tetrahedral (T) sheets sandwiching one octahedral (M) sheet54) of the muscovite lattice were allowed to relax during fitting. The vertical displacements of K+ ions in an interlayer and O atoms in a 2:1 layer were determined independently, whereas those of Si4+ (or Al3+) in T sites and Al3+ in M sites (specifically, in two M2 sites for dioctahedral micas such as muscovite) were determined as the average values of those of the coordinating oxygens and a hydroxyl.38 The structure of the interfacial water was expressed by a layered-water model.20,55 8639


Langmuir ubar (Å)

3.96 4.55 2.23 1.96 1.97 2.86 2.67 3.67

a

zj, cj, and uj: height from the muscovite surface, occupancy, and distribution width of the jth peak (j = 1−3). zw, dw, and uw: height of the first water peak from the muscovite surface, distance between two water peaks, and distribution width of the first water peak. ubar indicates how the distribution width increases for successive water peaks away from the muscovite surface.20,55 Occupancies (cj) are expressed in the dimensionless unit of water equivalents, Weq, the effective number of water molecules required to obtain the electron density of a peak (i.e., the electron density normalized to the number of electrons in H2O molecules per AUC). f: fixed during the fit. The number in parentheses after each parameter indicates the 1σ standard deviation of the last digit(s).

0.91(9) 1.08(16) 0.99(13) 1.13(24) 1.11(5) 1.60(25) 0.93(13) 2.35(23)

uw (Å) dw (Å)

2.26(29) 2.48(49) 2.29(40) 2.32(78) 2.64(2) 3.62(43) 2.33(52) 5.21(42) 8.20(11) 7.87(21) 8.00(12) 7.85(18) 9.77(11) 8.55(19) 6.24(15) 7.86(34) 1.20(13) 1.16(16) 1.10(12) 1.11(10) 1.60(9) 1.00(12) 2.11(94)

u3 (Å) c3 (Weq)

6.16(57) 5.58(75) 5.63(63) 5.27(70) 7.18(45) 3.85(57) 0.54(38) 5.15(7) 4.90(13) 5.19(9) 5.15(12) 6.32(6) 5.40(9) 8.74(99)

z3 (Å) u2 (Å)

0.62(5) 0.64(7) 0.73(4) 0.64(3) 0.95(3) 0.48(9) 1.20(15) 1.76(12) 5.48(32) 5.25(50) 5.77(32) 5.13(19) 7.09(25) 2.97(66) 6.01(83) 8.24(120)

c2 (Weq) z2 (Å)

2.33(2) 2.23(4) 2.37(2) 2.39(2) 2.63(3) 3.25(11) 3.49(12) 3.53(13)

third peak second peak

u1 (Å) c1 (Weq) χ (R factor) sample

mu3Li mu30Li mu3Na mu30Na mu3H3O mu3K mu3Rb mu3Cs

z1 (Å)

0.13(f) 0.13(f) 0.13(f) 0.13(f) 0.13(f) 0.47(10) 0.25(1) 0.21(1)

zW (Å) 8640

first peak

Table 2. Parameters for Solution Species in the Interfacial Region from the Best-Fit Models of the X-ray Reflectivity Dataa

3. RESULTS 3.1. X-ray Reflectivity Data. We first assess qualitatively how the solution composition affects the interfacial structure by comparing the normalized reflectivity of the muscovite (001) surface measured in alkali chloride and pH 2.5 HCl solutions to that measured previously in deionized water (pH near 5.7).55 The most prominent changes in intensity were observed for the experiments with Rb and Cs, the ions with the largest atomic numbers (Figure 1). The changes in reflectivity were smaller for systems containing lighter cations but were still visible near a normalized reflectivity minimum at q = ∼1.5 Å−1 and also at a maximum at q = ∼4 Å−1. All data presented were determined to high precision (i.e., a 1σ uncertainty in intensity of less than 2% for most data points except those around reflectivity minima where intensities are near 10−10; see the reflectivity plots before normalization in Figure S1). Therefore, even modest (e.g., 10− 20%) changes in reflected intensity are statistically significant and indicate changes in the interfacial structure. The XR data measured in the HCl solution at pH 2.5 deviate from those in DIW,55 indicating a difference in interfacial structure between these two systems. 3.2. Interfacial Solution Structure with Adsorbed Monovalent Cations. We establish the muscovite interfacial solution structure for individual experimental systems on the basis of the best-fit models of the X-ray data. The parameters and uncertainties that describe the interfacial profiles are listed in Table 2. There are significant and systematic changes in the profiles depending on the adsorbed ion. All profiles are

0.83(13) 0.44(17) 0.58(11) 0.77(7) 0.35(7) 2.81(66) 3.25(14) 4.13(1)

where cRb,j, zRb,j, and uRb,j are the occupancy, height from the surface, and rms distribution width of the jth Rb peak. The RAXR data for the RbCl solution were fit using one-peak and two-peak models, and a model composed of one Gaussian peak followed by a diffuse profile (details in Section3.2.5 and the Supporting Information). To confirm the validity of the models, fitting results were compared to the result from a model-independent analysis51 in which the q-dependent partial structure factor was expressed as AR(qn) exp[iΦR(qn)] using the amplitude (AR) and phase (ΦR) (SI). The parameters of the structural model were optimized using leastsquares fitting. The best-fit model was selected on the basis of the smallest χ2 (= Σk[(Ik − Icalc,k)/σk]2/(N − Np), where Ik and Icalc,k are the measured and calculated intensities, respectively, σk is the measured uncertainty of the kth data point, and N and Np are the numbers of data points and parameters used in the model-fit, respectively). The R factor (= Σk(|Ik − Icalc,k|/Ik)/N) of the best fit is also reported for comparison. On the basis of the best-fit model, the solution profile above the muscovite surface is plotted as a function of height from the surface. (The origin is chosen as the average height of basal surface oxygen.) All density profiles are broadened by the experimental resolution (∼0.6 Å corresponding to qmax = 5.3 Å−1).50 The electron density was normalized to that of bulk water (∼0.33 electrons/Å3) and expressed as water equivalents (Weq), the electron density normalized to the number of electrons in H2O molecules per AUC.38

0.99(3) 0.94(9) 1.19(5) 1.23(3) 0.66(9) 1.91(12) 1.96(2) 2.26(1)

water model

(3)

2

⎡ (q uRb, j)2 ⎤ ⎥ FRb(qn) = ∑j c Rb, j exp(iqnz Rb, j) exp⎢ − n ⎥⎦ ⎢⎣ 2

(0.072) (0.070) (0.064) (0.048) (0.064) (0.074) (0.059) (0.074)

In the RAXR data analysis,51 the resonant structure factor at a momentum transfer qn, FR(qn, E), can be separated into two independent terms. The E-dependent anomalous dispersion, f ′(E) + if ″(E), was experimentally determined on the basis of the Rb K-edge X-ray absorption near-edge structure measured in transmission mode through a 0.1 m RbCl solution followed by the differential Kramers− Kronig transform.56 The q-dependent partial structure factor of Rb is given by

0.50(f) 0.50(f) 0.50(f) 0.50(f) 0.22(4) 1.00(f) 0.69(21) 1.00(f)

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compared to that of muDIW55 to visualize the changes in the structure of hydration layers near the muscovite surface caused by the coverage and hydrated state of adsorbed cations. 3.2.1. Muscovite−HCl Solution Interface. The derived electron-density profile of the muscovite−solution interface in 3 × 10−3 m HCl (mu3H3O experiment; here we label each experiment according to the cation, with the numerical prefix corresponding to the cation concentration in 10−3 m; see Table 1) is different from that of the muscovite−deionized water interface (muDIW, Figure 3a). The muDIW profile has two sharp peaks 1.3 and 2.5 Å away from the surface, whereas the mu3H3O profile has one broad peak at ∼2.7 Å (Figure 3a). An attempt to fit the mu3H3O data using sharper peaks resulted in fit parameters with larger uncertainties (Figure S2 in SI), with only marginal improvement in the quality of the fit (χ2 decreased from 1.97 to 1.96). These fit parameters also were highly correlated (Pearson’s correlation coefficient, r2 > 0.9), indicating that they were not uniquely determined. The best-fit model (Table 2) has a small peak at 0.66 ± 0.09 Å that is not visible in Figure 3a, resulting in the partial overlap of the electron density of the solution with that of muscovite. This result indicates that some solution species may be located close to the surface in the ditrigonal cavity. An attempt to fit the data without the small peak (Figure S2) resulted in a poorer quality of fit (i.e., χ2 increased from 1.97 to 2.30), implying that this overlapped electron density is statistically significant. The mu3H3O profile also has a broad peak at 6.32 ± 0.06 Å whereas the solution profile about 11 Å above the surface is similar to that of muDIW. 3.2.2. Muscovite−LiCl Solution Interface. The electrondensity profiles of mu3Li and mu30Li (Figure 3b) show the largest changes from that of muDIW at heights of between 1 and 3 Å. Smaller changes are observed at heights greater than 4 Å. In these systems, the main contribution to the near-surface electron-density change is from water because Li+ is essentially invisible to X-rays. The electron-density profiles for the two Li+ concentrations (3 × 10−3 and 3 × 10−2 m) differ mainly in the occupation of the first peak at a height of around 1 Å (i.e., the higher-concentration mu30Li profile has a lower occupancy) and small differences in the structured water profile at heights of between 5 and 10 Å. The first peak is located approximately 0.3 Å closer to the surface and also has a substantially reduced occupation (in terms of Weq) compared to the first peak in muDIW55 (Table 2). Both LiCl profiles have a second peak located at 2.2−2.4 Å with a greater electron density than that of the first peak. This second peak is intrinsically broad, suggesting a dynamic distribution of species and/or the presence of multiple water species whose height differences were indistinguishable within the experimental resolution (∼0.6 Å). The peak at around 5 Å also has a slightly greater electron density than that in DIW. 3.2.3. Muscovite−NaCl Solution Interface. The interfacial profiles measured in 3 × 10−3 and 3 × 10−2 m NaCl are almost identical but differ from that measured in DIW for heights of less than ∼7 Å (Figure 3c). The electron density near 1.2−1.3 Å is slightly lower than that of muDIW, whereas that at 2.0−2.3 Å is higher. This pattern is similar to those observed in LiCl solutions (Figure 3b). In the NaCl profiles, however, some of the electron density may be from Na+, which has the same number of electrons as an H2O molecule. The NaCl profiles show an enhanced electron density in the region of 5 to 6 Å, similar to that in the LiCl profiles.

Figure 3. Electron-density profiles at the muscovite (001)−solution interface for (a) mu3H3O, (b) mu3Li and mu30Li, and (c) mu3Na and mu30Na. See Table 1 for sample labels. The electron-density profile for muDIW (cyan short-dashed curves)55 is also shown for comparison. The profiles are plotted as a function of the height from the average muscovite surface oxygen position. The electron density was normalized to that of bulk water and plotted with a band indicating the derived ±1σ uncertainty of the density45 as a function of height. The electron-density profile below 0 Å is not shown.

3.2.4. Muscovite−KCl Solution Interface. The total electron-density profile in the KCl solution has three peaks near the surface (Figure 4a). The two peaks closest to the surface are intrinsically broad (Table 2) and partially overlap. The occupancy of the first peak (2.81 ± 0.66 Weq/AUC) is larger than the maximum theoretical occupancy of water molecules located in the ditrigonal cavities (i.e., 2Weq/AUC), suggesting that this peak includes K+ ions. (See Section 4.1.2 for the estimation of the K+ occupancy.) The relatively large uncertainty of the first peak’s occupation parameter is mostly due to the overlap of the peak with the second peak at 3.25 Å. The heights of these two peaks (1.91 ± 0.12 and 3.25 ± 0.11 Å) are approximately 0.6−0.7 Å greater than those in the muDIW profile (Figure 4a).55 The third peak at 5.40 ± 0.09 Å is located farther from the surface and is narrower than that in DIW. 8641


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the adsorbed Rb+ has a narrow vertical distribution near the interface (eq 3). The best-fit structures using two-peak models show that Rb+ adsorbs in two states (Table 3). Most Rb+ is located in a narrow peak that is 1.97 ± 0.01 Å above the surface with a coverage of 0.78 ± 0.01 atom/AUC. This sorption height is slightly lower than the height (2.33 ± 0.10 Å) measured previously in a 1 × 10−2 M RbCl solution.23 A minor fraction of Rb+ is distributed farther from the surface (centered at around 7 to 8 Å) with a coverage ranging from 0.06 ± 0.01 to 0.11 ± 0.03 atom/AUC, depending upon the choice of the model. The shape and vertical distribution width of the second species are not well constrained by the data (SI), resulting in the large uncertainty of the estimated coverage. The total amount of Rb+ satisfies about 85−90% of the layer charge of the muscovite surface, in good agreement with the results from an isotherm measurement for Rb+ uptake by the muscovite surface at pH 5.5.47 The remaining charge could be compensated by Rb+ in a more extended diffuse profile (e.g., the Debye length of a diffuse profile is about 56 Å in the given experimental system based on the linearized Poisson−Boltzmann theory;57 see Section 4.1.2 for further discussion) and/or by adsorbed H3O+, to which the present data are insensitive. 3.2.6. Muscovite−CsCl Solution Interface. The derived electron-density profile in the CsCl solution shows a sharp, high electron-density peak at 2.26 ± 0.01 Å (Figure 4c). The position of the peak is similar to those observed previously in 1 × 10−2 and 5 × 10−1 m CsCl solutions (2.16 ± 0.02 and 2.15 ± 0.09 Å, respectively).20 The occupancy of the peak is significantly larger than that expected for water, indicating the adsorption of Cs+ at the interface. This peak partially overlaps with a broad electron-density peak centered at ∼4 Å. The overall density of this broader peak is slightly greater than that of deionized water, implying a possible contribution from outer-sphere (OS) Cs+. Farther from the surface the profile flattens, indicating that interfacial hydration layers are less ordered in the CsCl solution compared to all other solutions. 3.3. Surface Relaxation. The near-surface atoms in muscovite were observed to shift systematically to a depth of 40 Å (or four 2:1 layers). The results for all monovalent ions show a trend in which each 2:1 layer expanded (i.e., the deeper oxygen atoms moved into the crystal and the shallower oxygen atoms moved toward the surface; Figure 5a) by ∼0.05 Å. Note that these XR results are sensitive to lattice displacements with values as small as ∼0.02 Å.20,38 Similar trends were observed for muscovite in a 5 × 10−3 m BaCl2 solution.38 An exception to this trend was observed in the top 2:1 layer (i.e., the layer in direct contact with the aqueous solution), where the displacements of oxygen atoms were cation-dependent. (See Section 4.4 for a detailed discussion.) The interlayer K+ ions also moved systematically from their bulk lattice sites. They were displaced toward the surface with respect to their idealized bulk crystallographic positions,20 with the magnitude of the displacements decaying with depth (Figure 5b). This trend was fit to an exponential function {∝ exp(−κ|zKm|), where |zKm| is the depth of an interlayer K+ in the mth layer from the surface (m = 0, 1, 2, and 3) and 1/κ is a decay length (Å)} (Figure 5b). The derived 1/κ values range from 13 to 24 Å (with an uncertainty of ±1−5 Å), indicating that the K+ ion relaxations extended to significant depths below the surface.

Figure 4. Electron-density profiles for (a) mu3K, (b) mu3Rb, and (c) mu3Cs compared to that for muDIW.55 For mu3K and mu3Cs, the profiles of inner-sphere (IS) K+ and Cs+ are estimated on the basis of a space-filling constraint, and the net hydration profile is obtained by subtracting the estimated electron density of K+ from the total electron-density profile (details in the SI). For mu3Rb, the Rb-specific electron-density profiles are derived from the best-fit models (twopeak model A (2pk A), two-peak model B (2pk B), and one-peak and diffuse model (1pk + diffuse); refer to Table 3 for the parameters) of the RAXR data. Refer to Figure 3 for a description of the axes. The distribution profile of outer-sphere (OS) Rb+ is scaled by a factor of 5 for better visibility. The net hydration profile is calculated by subtracting the Rb+ density from the total electron-density profile.

3.2.5. Muscovite−RbCl Solution Interface. The total electron-density profile of mu3Rb has a high electron-density peak at 1.96 ± 0.02 Å above the muscovite surface (Figure 4b). The occupancy ((3.25 ± 0.14)Weq) is significantly larger than that obtained solely from water, suggesting that a large fraction of the peak density is from adsorbed Rb+. The Rb+-specific profile was obtained from the RAXR spectra (Figure 2), which show characteristic intensity variations near the X-ray K-edge absorption energy (Eo) of Rb. Relatively large signals are maintained up to the highest q value, indicating that some of 8642


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Table 3. Parameters for the Distribution of Rb+ in the Interfacial Region in a 3 × 10−3 m RbCl Solution Derived from the BestFit Models of the RAXR Dataa inner-sphere Rb+ models

χ (R factor)

zIS

one-peak model two-peak model A two-peak model B

1.50 (0.0098) 1.30 (0.0096) 1.28 (0.0096)

1.97(1) 1.97(1) 1.97(1)

2

cIS

outer-sphere Rb+ uIS

zOS

0.76(1) 0.15(5) 0.78(1) 0.19(4) 0.78(1) 0.19(4) inner-sphere Rb+

7.29(24) 7.84(37)

cOS

uOS

0.06(1) 0.11(3) diffuse Rb+ profile

1.00(f) 2.17(44)

model

χ2 (R factor)

zIS

cIS

uIS

zdif

cdif

κ−1dif

one-peak + diffuse model

1.26 (0.0095)

1.97(1)

0.79(1)

0.21(4)

6.33(42)

0.12(5)

3.0 (15)

z, c, and u: height (Å) from the muscovite surface, occupancy (atom/AUC), and distribution width (Å) of a Rb+ peak. zdif, cdif, κ−1dif: height of the first peak (Å), total occupancy (atom/AUC), and Debye length (Å) of a diffuse Rb+ profile. f: fixed during fit. The number in parentheses after each parameter indicates the standard deviation of the last digit(s). a

alkali cations behave differently at the interface. Cation adsorption affects the interfacial hydration structure within about 15 Å of the muscovite surface and the relaxations in the muscovite structure within 40 Å from the surface. It is our thesis that these individual observations are all interconnected, and controlled ultimately by the ion size and its influence on the ion hydration structure and hydration strength, which directly determine the specific coverage and speciation of the adsorbed cations. 4.1. Adsorption Speciation of Alkali Metal Cations. 4.1.1. Li+ and Na+. The adsorption of Li+ at the muscovite surface can be inferred by observed differences in the occupancy of water given that Li+ is practically invisible to Xrays. The occupancy of the peak at approximately 1 Å in the electron-density profiles for the LiCl solutions decreases on a Weq basis with increasing Li+ solution concentration from 0 (muDIW) to 3 × 10−3 (mu3Li) to 3 × 10−2 m (mu30Li) (Table 2). The decrease in peak occupancy indicates that water molecules may be displaced from the ditrigonal site by the adsorption of Li+. The small Li+ ion (ionic radius of 0.59−0.74 Å depending on the coordination number)58 could penetrate deeply into the ditrigonal cavity if dehydrated. The electrondensity profile of the solution adjacent to the muscovite surface overlaps slightly with that of the surface oxygens in muscovite. This may indicate the presence of partially hydrated IS Li+ in the ditrigonal cavity. The decrease in the occupancy of water in the first electron-density peak may occur when a fully hydrated Li+ adsorbs above a ditrigonal cavity, leaving the interior of the cavity inaccessible to other water molecules.59,60 The outersphere adsorption of Li+ is expected to dominate because Li+ has a large free energy of hydration compared to other monovalent cations.3,5,61,62 The enhanced electron density near 2 Å for both LiCl solutions (Figure 3b) may be related to water molecules coordinated to OS Li+. The coexistence of IS and OS Li+ species on the muscovite surface is supported by results from a recent MD simulation.31 The solution profiles within 4 Å of the surface for the NaCl experiments are similar to that for the DIW data.55 We would expect to see some change in the structure if Na+, a cation with the same number of electrons as H2O, were adsorbed as an IS complex but at a height different from that of H2O (1.3 Å).55 The predicted height of dehydrated Na+ adsorbed in the ditrigonal cavity is 0.6−1.1 Å for close-packed coordination with an effective Na+ radius of 1−1.2 Å.58 Neither Na+ solution profile has a distinct peak at this height, indicating no substantial adsorption of IS Na+ at this position. Results of MD simulations31 and a subsequent XR study42 by Sakuma et

Figure 5. (a) Vertical displacements of oxygen atoms in the top two unit cells below the muscovite (001) surface in contact with various solutions containing monovalent ions. The top schematic shows the atomic structure of the muscovite near the (001) surface, and red and purple spheres indicate oxygen (or hydroxyl) and interlayer K+, respectively. Positive and negative displacements indicate movements of atoms toward the solution and into the bulk crystal, respectively. (b) The observed exponential decay of vertical displacements of interlayer K+ is shown as a function of depth for the different cations with the same color/symbol code as in part a.

4. DISCUSSION The observed variations in the interfacial electron-density profiles are more complicated than might be expected by assuming simple cation substitutions at specific surface sites such as ditrigonal cavities. The complexity results from other factors including the difference in coverage and sorption geometry of adsorbed cations. The solution structure in the HCl solution is distinct from all others, indicating that adsorbed H3O+ (or, more generally, hydration products of H+) and the 8643


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4.1.2. K+, Rb+, and Cs+. The interfacial structures of muscovite in contact with solutions containing K+, Rb+, and Cs+ all show strong evidence of the dominant location of the adsorbed cation in terms of the large electron-density peak near 2 Å. The location is apparent because of the relatively large atomic numbers and general similarity in adsorption geometry of these ions. The solution electron-density profile in the KCl experiment is different from that of DIW.55 The derived adsorption height (1.91 ± 0.12 Å) for K+ is slightly greater than those for K+ (1.67 ± 0.06 and 1.77 ± 0.07 Å) previously measured by XR at higher KCl concentrations (0.01 and 0.5 m, respectively).20 The K+ position is also slightly farther from the basal oxygen plane than K+ in the bulk crystal (1.7 Å).20 This XR measurement does not distinguish electron-density contributions of the surface hydration layer from those of the adsorbed K+ ions; consequently, it may reflect changes in either aspect of the structure. An outward shift of 0.36 Å was predicted by first principles MD simulations upon hydrating a dry K+ ion on the muscovite (001) surface with 12 water molecules66 and was interpreted to be caused by the partial solvation of IS K+. The second peak at ∼3.25 Å is intrinsically broad and may contain both the primary hydration layer above the muscovite surface and the water molecules that hydrate the IS K+.28 The adsorption height of IS Rb+ measured by RAXR (1.97 ± 0.01 Å, Table 3) is greater than all previously measured IS K+ heights (Table 2 and ref 20). The adsorption height difference is consistent with the larger size of Rb+ with respect to that of K+ (i.e., ionic radii of 1.52 vs 1.38 Å, respectively, in octahedral coordination with oxygen).58 The Cs+ ion is larger (1.67 Å in octahedral coordination with oxygen)58 than K+ and Rb+ and adsorbs at 2.26 ± 0.01 Å, farthest from the surface among these cations. The peak position matches those previously measured for the muscovite surface in 1 × 10−2 and 5 × 10−1 m CsCl solutions (2.15 ± 0.09 and 2.16 ± 0.02 Å, respectively).20 This height agrees with the adsorption height predicted for IS Cs+ (∼2.0−2.2 Å) by Monte Carlo (MC) simulations.27 Our results indicate that the IS coverage of monovalent cations increases systematically with decreasing cation hydration energy.14,61 The coverage of IS K+, estimated using a space-filling constraint20,38 (see the SI for a description), is ∼0.6 atom/AUC (Figure 4a). The occupancy of IS Rb+ estimated on the basis of the space-filling constraint is ∼0.8 atom/AUC, which is consistent with the value of 0.78 ± 0.01 atom/AUC obtained directly from the RAXR data. The coverage of IS Cs+ estimated by the space-filling constraint is ∼0.9 atom/ AUC. The coverage of IS K+ is less than that of Rb+ or Cs+, perhaps because some K+, which has a larger hydration free energy than Rb+ and Cs+,62 may also adsorb as an OS complex. The RAXR data show that a small fraction of Rb+ also adsorbs as an OS complex. Compared to these cations, the Cs+ ion tends to adsorb mostly as an IS complex, presumably because the energy cost for displacing water molecules from the cation hydration shell of the OS complex is smallest.5 This is consistent with our interpretation that Li+ and Na+, which have even larger hydration free energies than the heavier alkalis,62 adsorb mainly as OS complexes. The XR results for the adsorption of K+ disagree with results from recent MC simulations.30 The simulation results predict two K+ species near the interface: an IS complex coordinated to an oxygen triad located at ∼2.15 Å above the surface and an OS complex located at 4.4−5 Å. The simulated IS adsorption height is inconsistent with the height (1.91 ± 0.12 Å) that we

al. at higher NaCl concentrations (0.6 m and 0.5 M, respectively) show IS Na+ at 1.6 Å, but we observed no distinct peak in our Na+ solution profiles at this position (Figure 3c). This apparent discrepancy is most likely the result of different modeling approaches for the reflectivity data rather than an intrinsic difference in system behavior. In the previous XR study,42 the peak at 1.6 Å largely overlaps with the next peak at 2.8 Å, forming an overall broad peak centered at ∼2.3 Å (i.e., the weighted-mean height), which matches the height of the second peak for our mu3Na and mu30Na data (Table 2). The overall occupancy of the two peaks {1.27 e − /Å 2 corresponding to 5.93 Weq (= 1.27 × AUC/10, where 10 is the number of electrons in one H2O); uncertainty not reported in the original article42} is also comparable to those for mu3Na and mu30Na {(6.35 ± 0.34)Weq and (5.90 ± 0.20)Weq, respectively, Table 2}. However, this result does not prove, although it is consistent with, the conclusion that the Na+ coverages are similar in these three systems because the exchange of Na+ for H2O (or H3O+) at the interface does not change the overall number of electrons at the interface. Other MD simulations of the basal surface of smectite (a clay mineral with structure similar to that of muscovite but a smaller lattice charge) in contact with mixed NaCl−CaCl2 solutions having total Cl− concentrations of 0.34−1.83 M were performed by Bourg and Sposito.63 These simulations showed a small fraction of partially hydrated Na+ ions in an IS state, located relatively far (∼2.5 Å) from the surface. This adsorption height is similar to the range where we found electron-density peaks in NaCl solutions. This height range is also near that (∼2 Å) expected for IS Na+ adsorbed above the center of the oxygen triad of an inverted SiO4 (or AlO4) tetrahedron. Frequency-modulated atomic force microscopy (FM-AFM) images of the muscovite (001) surface in 150 mM Li+ and Na+ solutions show protruding features in hexagonal arrays near the surface.25 These features were interpreted to be Li+ and Na+ adsorbed above the tetrahedra on the basis of an assumption that all water molecules were removed by the AFM tip.25 However, it is unlikely that the tip displaces water without perturbing the adsorbed cations, especially for the case of strongly hydrated Li+ and Na+.62 Moreover, the IS adsorption of cations on top of SiO4 or AlO4 tetrahedra should be energetically less favorable because of the proximity of the lattice cations (Si4+/Al3+) (i.e., ∼2.6 Å in this face-sharing geometry compared to ∼3.6 and ∼4.1 Å for Li+ and Na+, respectively, in a corner-sharing geometry).20,62,64,65 The enhanced electron density at 2.0−2.3 Å that we observed in both LiCl and NaCl solutions can be explained in terms of the location of the hydration shell of adsorbed OS (OSads) cations. Outer-sphere adsorption is the most energetically favorable geometry for strongly hydrated cations.5 Water is tetrahedrally coordinated around Li+, and Na+ has 5.2 water molecules (on average) in its first hydration shell with coordination geometries of between trigonal bipyramidal and square pyramidal, based on ab initio MD simulations.64,65 When hydrated Li+ or Na+ ions approach the surface without the disruption of their first hydration shell, some of their associated water molecules (e.g., three for Li+ or three or four for Na + ) are positioned near the muscovite surface. Calculations based on the closest packing of these hydrated ions predict that the average heights of the oxygens in the water molecules closest to the surface range from 2.1 to 2.5 Å, consistent with the observed heights of the largest peaks in the Li+ and Na+ solution electron-density profiles. 8644


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Inherently fast proton dynamics at the interface could lead to an interfacial structure that is more diffuse than those in which other monovalent cations are localized in several specific states (i.e., IS and OS species). Protons in hydronium are highly mobile because of the extremely low energy needed to transfer protons between adjacent water molecules.40 Numerous molecular structures can exist during “proton hopping” (e.g., H9O4+ (Eigen complex) and H5O2+ (Zundel complex)). Calculations using ab initio path integral simulations suggest that the proton-transfer reaction is controlled by the disruption of the secondary hydration shell around a hydronium ion, whose effective free energy barrier is ≤0.6 kJ/mol.41 The electron-density profile from XR represents an atomic-scale structure that is averaged both laterally over the macroscopic beam footprint (approximately a few square millimeters) and temporally over the measurement time (seconds to minutes). Therefore, the resolution of hydronium dynamics at the interface is not possible from the data. The interfacial electron-density profile of the HCl solution at pH 2.5 is also different from that of deionized water at pH 5.755 at heights of up to ∼11 Å above the surface. The concentration of hydronium at pH 2.5 is about 1500 times greater than at pH 5.7. Thus, the interfacial system at pH 5.7 can be intrinsically different from that at pH 2.5 because adsorbed hydronium may not saturate the surface charge of the muscovite at nearly neutral pH. In fact, the estimated coverage of hydronium at pH 5.7 is only 20% using an empirical adsorption constant of hydronium on the muscovite (001) surface.47 We infer that there is little to no adsorbed K+ in deionized water at pH 5.7 by comparing the XR data and associated total electron-density profile with those in the KCl solution (Figures 1 and 4a). The complete desorption of K+ has been demonstrated using 39K NMR spectroscopy from a pH 1 HCl solution−nanocrystalline muscovite mixture with a solid-solution mass ratio of 1 (i.e., at H3O+/K+ = 0.8).24 In the previous muDIW experiment, the H3O+/K+ ratio was sufficiently large (∼100)55 to achieve a preferred adsorption of H3O+ over K+. The result also identifies the presence of solution species located at 0.66 ± 0.09 Å. This feature likely represents the position of oxygen in H2O or H3O+, whose difference cannot be distinguished because hydrogen is almost invisible to X-rays. The ditrigonal cavity may be distorted laterally (e.g., by a tetragonal rotation54) to allow the molecule to approach the surface more closely than the height of water reported in deionized water.55 Further interpretation was not possible because the occupancy of the peak is relatively small and the current specular XR data do not provide information on any lateral distortions. 4.3. Hydration Structure at the Muscovite−Solution Interface. The electron-density profiles show that the solution structures near the muscovite surface vary systematically with the choice of adsorbed cation. For Li+ and Na+ solutions, the profiles are similar to that of muDIW,55 indicating that the hydration structure near the muscovite surface was mostly unchanged. The relatively small change near the surface may result from the lower surface coverage15 and/or the dominant OS adsorption of these cations. The mu3K profile has a peak at around 3.3 Å. This peak is ∼0.8 Å farther from the muscovite surface than the second water peak (at a height of ∼2.5 Å) of muDIW and can be related to water molecules coordinated to IS K+ adsorbed in the ditrigonal cavity.66 The electron-density profiles of the net hydration for mu3Rb and mu3Cs show that the interfacial hydration layers are, on average, less structured

observed by XR and with the previously determined heights closer to the surface.20 The OS species was interpreted to be transient, existing only during desorption or diffusion processes, because the predicted free-energy difference between the IS and the OS states was large (45−48 kJ/mol).30 Although we do not have any direct evidence for the location of an OS K+ species, the mu3Rb results provide some insight into the free-energy difference between the IS and OS complexes of the other alkali metal cations. The RAXR data show that a small fraction (7− 12%) of Rb+ adsorbs as an OS species. The free-energy difference between IS and OS Rb+ can be estimated to be from −5 to −6 kJ/mol (= −RT ln(cIS/cOS), where R is the gas constant, T is room temperature, and cIS and cOS are the coverages of IS and OS Rb+ species, respectively). The freeenergy difference between IS and OS K+ is expected to be smaller than this value5 because the hydration free energy of K+ is larger than that of Rb+.37,67 This interpretation agrees with the lower coverage of IS K+ that was observed by XR. Assuming full charge compensation, the nominal IS K+ coverage (0.6 atom/AUC) should be complemented by about 0.4 atom/AUC of K+ as an OS species, which would suggest a free-energy difference of around −1 kJ/mol (= −RT ln(0.6/0.4)) between the two species. Our identification of two adsorbed Rb+ species in this study is distinct from the results in a previous RAXR study in which only one Rb+ species was reported to adsorb on the muscovite surface.23 The adsorption height of the second Rb+ species (about 6−8 Å, Table 3) is large compared to that of any adsorbed OS complexes of divalent cations (3.5−4.6 Å) on the muscovite surface5,23,39,45 but is similar to those of extended OS (OSext) complexes of the divalent cations (5.4−9.6 Å).5 The OSext species are interpreted as having multiple intervening waters between the cation and the surface.5 The OSext species are typically distributed more broadly, reflecting their greater mobility. The OSext Rb+ species identified here may be related to the diffuse ion profile. Simulations of the EDL on the basal surface of smectite63 show that a small amount of Na+ exists at heights ranging from 5 to 9 Å. In particular, the Na+ ions located closest to the surface in this distributed profile were stabilized at the interface by two layers of water (i.e., one from the first hydration shell of Na+ and the second overlapping with the interfacial hydration layer of the smectite surface).63 The distribution height of this Na+ profile matches that of OSext Rb+ despite the differences in the hydration energy37,67 and structure13,62,64,65 between the two cations. We attempted to fit the OSext Rb+ distribution using a diffuse profile (Table 3 and SI). The resulting Debye length of 3.0 ± 1.5 Å (the relatively large uncertainty is mainly due to the scarcity of low-q data) is significantly shorter than that (∼56 Å) calculated by the classical linearized Poisson−Boltzmann model57 but is similar to the normalized Gouy−Chapman length (∼5 Å) calculated from ion condensation theory.9 4.2. Sorption of Hydronium at the Muscovite− Solution Interface. The adsorption behavior of hydronium at the muscovite surface in pH 2.5 HCl solution is distinct from that of the alkali metal cations. The electron-density profile shows only relatively diffuse features near the interface (e.g., at ∼3 Å) without any sharp peaks to indicate the presence of either distinct adsorbed species or well-ordered hydration layers. As for Li+, the XR measurement is insensitive to the location of the protons in H3O+ but instead probes changes in the interfacial hydration structure resulting from the presence of hydronium. 8645


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surface are arranged differently than in the bulk crystal. Within the crystal, the tetrahedral and octahedral sheets are considerably distorted because of the misfit between octahedral and tetrahedral sheets.54 As a result, the site containing interlayer K+ normally has a ditrigonal shape instead of an ideal hexagonal geometry. However, the AFM images showed that ditrigonal cavities at the cleaved surface exposed to DIW were transformed to a more hexagonal shape, with all inner angles at ∼120° but with two opposing edges more elongated than the others.35 Larger displacements are expected to occur in muscovite perpendicular to the basal plane rather than within the plane because of the relatively weak ionic interactions between the basal oxygens and interlayer ions. The XR data show that these internal structural relaxations generally extend 30−40 Å below the exposed surface (Figure 5a) as observed earlier.20,38 The present results allow a more precise determination of the systematic trends in the near-surface relaxation of the muscovite lattice. The substrate K+ ions are displaced systematically toward the surface with a magnitude that decays exponentially below the surface (Figure 5b). This trend suggests that the negative surface charge exerts an electrostatic field not only into the solution but also into the solid. Displacements of K+ lattice ions in the crystal toward the cleaved surface may be caused by electrostatic attraction toward the negative charge in the surface tetrahedral sheet. We observed an increase in the average distance between the basal and apical tetrahedral oxygen planes with respect to the bulk value20 (except for the outermost tetrahedral sheet in contact with aqueous solution as noted below), which was unexpected because the tetrahedral sheets in the bulk muscovite crystal are already elongated in this direction to reduce the misfit between tetrahedral and octahedral sheets.54,69 The observed vertical expansion may be related to a change in the tilt angles of tetrahedra in the tetrahedral sheets (Figure 6a). In general, the tetrahedra in dioctahedral micas are tilted by about 5 and 7° from their theoretical states because of the lateral translation of two apical oxygens, O4 and O5, to accommodate the size difference between two types of octahedral sites {i.e., M1 (unoccupied) and M2 (occupied by Al3+) sites in Figure 6b}.70 This distortion decreases the vertical distance between three basal oxygens (Ob) and one apical oxygen (Oa), the value of Δ⟨zOb − zOa ⟩tilting), and causes the corrugation of the (001) basal plane with the height of the O2 oxygens being lower by ∼0.22 Å than those of O1 and O3.20 The XR results, in contrast, show an increase in the distance between the basal and apical oxygens, indicating an untilting of the tetrahedra (i.e., movements of O4 and O5 toward O2 atoms in Figure 6a). This rearrangement makes the (001) plane less corrugated (i.e., more similar to that of most trioctahedral micas71) and also reduces the size of the octahedral vacancy (Figure 6b). The XR results also show that the octahedral sheets in the top layers of muscovite generally expand. In dioctahedral micas, including muscovite, the highly charged trivalent cations (e.g., Al3+) in the M2 sites repel each other, resulting in a lateral expansion of the entire octahedral sheet and a shortening of the shared edges (e.g., 2.3−2.5 Å for the observed shared edge lengths compared to 2.7−2.9 Å for the unshared edges).54,71 The shortening of shared edges requires oxygen atoms to move in directions diagonal to the plane of the sheet, so the entire octahedral sheet is also contracted along the sheet normal direction. However, near the cleaved muscovite surface we

compared to those of the other monovalent cations (Figure 4b,c). These two cations are less strongly hydrated,37,67 and their adsorption apparently disturbs the hydration layers near the muscovite surface. This result supports previous MD simulation results in which the amplitude of the interfacial water density oscillation decreases when Cs+ adsorbs on the muscovite surface.31 This result also appears to be consistent with surface force apparatus measurements that showed that no repulsive hydration force was observed between two muscovite (001) surfaces immersed in 0.1 M Cs+ solution whereas a strong repulsive force was observed in a comparable Na+ solution.32,33 Adsorbed cations also play a significant role in controlling the vertical long-range ordering of water at the interface.1,15,59 The total electron-density profiles show weak modulations in density extending up to ∼10 Å from the surface. The periodicities of these oscillations, modeled by a layered-water model,20,55 range from 2.3 ± 0.5 to 3.6 ± 0.4 Å (Table 2). These values agree with the values (e.g., 3.7 ± 0.3 Å in DIW55 and 2.7 ± 0.3 to 2.9 ± 0.3 Å in KCl solutions20) previously measured by XR. Some of the electron density can be related to OS cation species (including both adsorbed and extended OS complexes)5 that would be located farther from the surface because of the intervening water molecules between the metal cation and the surface. The formation of an extended water layer structure up to about 15 Å from the muscovite surface is likely controlled by the hydration strength of adsorbed ions. The adsorption of the more strongly hydrated Li+ and Na+ does not disturb structured water layers near the interface. Oscillatory features in the interfacial density profile appear to be most distinct and extended for mu3Li and mu3Na. The magnitude of the oscillations generally becomes weaker as the hydration energy of the adsorbed ion37,67 decreases. This change also can be caused in part by the difference in coverage of the cation. Li+ and Na+ were reported to adsorb weakly to the muscovite (001) surface compared to the other alkali cations.15 The total coverage of adsorbed cations for mu3Li and mu3Na may be insufficient to satisfy fully the layer charge of the muscovite surface. As a result, the muscovite surface may still possess residual negative charge, which induces the ordering of water dipoles near the interface. Conversely, the amount of adsorbed IS Cs+ for mu3Cs (∼0.9 atom/AUC calculated from the spacefilling constraint) effectively neutralizes the surface and therefore may weaken the ordering of water dipoles. A similar effect was observed in XR studies on hematite−water and corundum−water interfaces where water layers tend to be weakly ordered when the functional groups on the surface are largely uncharged.68 The electron-density profiles of mu30Li and mu30Na, in which the concentrations of solution cations were 10 times higher than for mu3Li and mu3Na, show diminished water oscillations compared to mu3Li and mu3Na. Although these changes are only marginally significant (compare these differences in profiles with the 1σ uncertainty bands43 of electron density in Figure 3b,c), they support the idea that water density oscillations are controlled in part by the magnitude of the local interfacial electric field. 4.4. Muscovite Surface Structure. The truncation of the (001) surface of muscovite and its exposure to aqueous solution cause atoms near the surface to relax their positions and bond angles in order to minimize the free energy of the system. High-resolution AFM studies35,36 on the muscovite (001) surface in contact with water showed that O atoms at the 8646


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Figure 7. Distortion of the top tetrahedral sheet in direct contact with solution. Δ⟨zOb − zOa⟩elongation indicates the magnitude in the tetrahedral elongation caused by the pure expansion or contraction of the tetrahedra perpendicular to the (001) surface. Δ⟨zOb − zOa⟩tilting indicates the change in the distance between the average heights of basal oxygens (Ob) and apical oxygens (Oa) along the surface normal direction. The tetrahedral (un)tilting angle, ΔΦ, corresponding to the Δ⟨zOb − zOa⟩tilting value is also shown. ΔΦ = 0 corresponds to no change in the tilting angle from the bulk structure (Figure S5), and a positive sign indicates an increase in the angle. See SI for the detailed calculation. Refer to Table 1 for sample labels. The values for muDIW were derived from two separate data sets. Gray arrows indicate trends observed for increasing solution concentrations for H3O+, Li+, and Na+, and a curved orange-brown arrow indicates a trend of decreasing hydration strength for K+, Rb+, and Cs+. Figure 6. Schematics showing the effect of tetrahedral untilting on the structure of (a) the tetrahedral sheet and (b) the octahedral sheet near the muscovite (001) surface. The relaxed muscovite (001) surface becomes more similar to those of typical trioctahedral micas (i.e., with a smaller corrugation of the basal oxygen planes (shown in a) and a reduced volume for the M1 site (shown in b). Red and brown spheres represent basal oxygens, blue spheres represent apical oxygens, lightgreen spheres represent hydroxyls, and small sky-blue spheres in b represent Al3+ in the octahedral M2 sites (light blue). A ditrigonal cavity is shown as a dashed black line for clarity. The crystallographic axes are indicated.

zOa⟩elongation) of the tetrahedral sheet in pH 2.5 HCl was larger than in systems of other monovalent cations but similar to that in DIW (Figure 7). This indicates that hydronium interacts with the surface differently than does other monovalent cations. Hydronium promotes the formation of a hydrogen-bonded network with the surface oxygen atoms that may tend to “pull” the surface oxygen atoms toward the solution. Such an interaction should be weaker for the other monovalent cations, especially for those that are less strongly hydrated. This is consistent with the results for the CsCl solution, which show a vertical contraction of the tetrahedral sheet. If the formation of a hydrogen-bonding network drives the expansion of the tetrahedra at the surface, then the result for the CsCl solution can be interpreted as a disruption of the interfacial hydration layer31−33 (Figure 4c) caused by the adsorption of more weakly hydrated Cs+ ions67 on the surface. The tetrahedral tilting of the outermost sheet is controlled by the cation adsorption coverage with a larger tilting displacement for a smaller cation coverage. We observed that surface tetrahedra are more tilted in DIW and 3 × 10−3 m LiCl and NaCl solutions. In water at pH 5.7, the amount of H3O+ adsorbed on the surface is insufficient for full charge compensation.47 Likewise, the adsorption of Li+ and Na+ on the muscovite surface is weaker than for the other monovalent cations,15 and it is likely that Li+ and Na+ coverages also were insufficient to satisfy the layer charge of the surface. The remaining surface charge would be balanced by cations in the diffuse layer, whose interaction with the surface is even weaker than that of the adsorbed cations. As a result, the surface structure, specifically, the tilting of the surface tetrahedra in this case, may deviate more strongly from the bulk structure. In contrast, our data from the K+, Rb+, and Cs+ experiments all

observed an expansion of the octahedral sheets, implying that the distortions of the octahedral sheets become smaller (i.e., the octahedral sheets become similar to those in trioctahedral micas). The transformation requires the screening of the electrostatic repulsion between two Al3+ ions in M2 sites and may be related to the change in orientation of the hydroxyls (which could not be determined from the XR data), which is caused by the change in the electrostatic field near the surface. The displacement of basal oxygen atoms in the surface tetrahedral sheet deviates from the trends observed for those of the second and deeper 2:1 layers (Figure 5a). The oxygen atoms in the outermost tetrahedral sheet are in direct contact with the adsorbed cations and water molecules and therefore are most strongly affected by the interfacial environment. The overall Δ⟨zOb − zOa⟩ values shown in Figure 5a are related to at least two distortions, tetrahedral elongation and tetrahedral (un)tilting. We attempted to fit the XR data by considering these two effects (SI) only for the oxygen atoms in the top sheet. The results show systematic trends in the atom relaxations of the top surface (Figure 7), suggesting that the relaxations are related to both the hydration energy and the coverage of an adsorbed cation. Vertical elongation (Δ⟨zOb − 8647


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Department of Energy under contract DE-AC02-06CH11357 to UChicago Argonne, LLC as the operator of Argonne National Laboratory and grants DE-FG02-06ER15364 and DEFG02-03ER15381. The reflectivity data were collected at beamlines 6-ID-B (MU-CAT) and 33-ID-D (UNI-XOR), Advanced Photon Source. Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract DEAC02-06CH11357 to UChicago Argonne, LLC as the operator of Argonne National Laboratory. We thank Dr. Moritz Schmidt for helpful discussion and two anonymous reviewers for their comments. The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under contract no. DE-AC02-06CH11357. The U.S. Government retains for itself, and others acting on its behalf, a paid-up nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government.

show smaller changes in tetrahedral tilting from the bulk value. The tilting angle decreases with increasing cation concentration in LiCl and NaCl solutions, indicating that the increased adsorption of these cations near the surface made the nearsurface muscovite structure more like that in the bulk crystal. A similar pattern occurs for the pH 2.5 HCl solution compared to that of pH 5.7 water.

5. CONCLUSIONS The muscovite−solution interfacial structure is determined by interactions among the adsorbed monovalent cation species, the interfacial hydration layer, and the substrate lattice at and below the surface. Cation-specific changes occur over a range of ∼50 Å across the interface, from about 15 Å above the surface in the solution to approximately 40 Å below the surface. Water plays an important role in determining the adsorbed states of cations at the interface. More strongly hydrated cations, such as Li+ and Na+, likely adsorb dominantly as OS complexes because of the larger amount of energy required for dehydration.5 The speciation and coverage of adsorbed cations affect the properties of interfacial hydration layers. Relatively well ordered interfacial hydration layers extending up to about 10 Å from the surface were observed in the presence of strongly hydrated Li+ and Na+, whereas the interfacial hydration layers became more disordered in the presence of the less strongly hydrated Rb+ and Cs+. The water profile within 5 Å from the surface in pH 2.5 HCl solution is even more diffuse, reflecting the greater mobility and continuous change in the hydrated configuration of protons at the interface. The adsorption of cations and the formation of the interfacial hydration layer also lead to vertical displacements of atoms near the muscovite surface. The observed vertical changes are expected to be closely coupled to lateral distortions, such as the tetrahedral rotations,36 and may lead to changes in sorption geometry (e.g., the effective coordination of adsorbed cations72). Therefore, these internal interatomic interactions need to be included more explicitly in computational studies. The interfacial structural characterization by XR can be beneficial in terms of developing more accurate models for computational studies73 and validating the force fields used for molecular simulations.

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ASSOCIATED CONTENT

S Supporting Information *

Detailed descriptions of X-ray reflectivity measurements. Temporal change in the RAXR signal of the mu3Rb data. Model fit of the mu3Rb RAXR data. Space-filling constraint analysis. Tetrahedral tilting and elongation calculation. X-ray reflectivity plot. Comparison of the electron-density profiles derived from two-peak and three-peak model fits for mu3H3O. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*Phone: (630) 252-6679. Fax: (630) 252-9570. E-mail: sslee@ anl.gov. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Geosciences Research Program, Office of Basic Energy Sciences, United States 8648


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