Surface Charge of the Calcite (104) Terrace Measured by Rb+

Jun 23, 2016 - (15, 45) From eq 5, the pKa value of Ca ions in the calcite terrace can be ...... Fenter , P. A. ; Rivers , M. L. ; Sturchio , N. C. ; ...
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Surface Charge of the Calcite (104) Terrace Measured by Rb+ Adsorption in Aqueous Solutions Using Resonant Anomalous X‑ray Reflectivity Sang Soo Lee,*,† Frank Heberling,‡ Neil C. Sturchio,§ Peter J. Eng,∥,⊥ and Paul Fenter† †

Chemical Sciences and Engineering Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, United States ‡ Institut für Nukleare Entsorgung, Karlsruher Institut für Technologie, P.O. Box 3640, 76021 Karlsruhe, Germany § Department of Geological Sciences, University of Delaware, Newark, Delaware 19716, United States ∥ Center for Advanced Radiation Sources and ⊥James Franck Institute, University of Chicago, Chicago, Illinois 60637, United States S Supporting Information *

ABSTRACT: Adsorption of Rb+ on the (104) plane of single crystal calcite was investigated to estimate the charge of the ionic crystal calcite−water interface. The adsorbed Rb+ coverage was quantified as a function of Rb concentration (1−100 mM) in calcite-saturated solutions at pH 8.3 by using in situ resonant anomalous Xray reflectivity in transmission cell geometry. The Rb+ coverages for all solution conditions were small with the maximum ion coverage (Γmax) of 0.12(4) Rb+/nm2 estimated by the best-fit Langmuir isotherm model. This result provides an estimate of the upper limit to the effective surface charge density of about −0.02 C/m2 considering that any Rb+ adsorption to the terrace plane is likely induced by electrostatic attraction. This charge density is significantly lower (by a factor of ≥10) than those estimated from macroscopic measurements, implying that any excess charge likely originates from surface defects.

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INTRODUCTION Calcite, CaCO3, the most dominant carbonate material in the earth’s surface environment, plays a key role in the global carbon cycle via both organic (biological) and inorganic processes.1−3 The reactivity of calcite also affects the chemistry of natural water, including the fate of dissolved metal ions.4−9 However, the nature of calcite surface reactivity, specifically the degree to which metal ion sorption is driven by adsorption vs (co)precipitation,10,11 has been the subject of a debate. It is relatively well-known that calcite surfaces are capable of incorporating ions through ion exchange reactions and growth of secondary phases at defect sites,7,9,12 but the issue of simple ion adsorption on a defect-free calcite surface (i.e., its terrace) is still unclear. Understanding the surface charge of calcite is key to clarifying the issue of surface absorption.10,13 The ideally terminated calcite (104) surface, the dominant cleavage plane (Figure S1 of the Supporting Information), exposes equal numbers of Ca2+ and CO32−, thereby stoichiometrically neutral.14,15 In aqueous conditions, however, it has been suggested that the surface can develop charge via hydrolysis of water molecules bound to surface Ca2+ ions and/or protonation of the surface carbonate groups.11,16,17 This charge development mechanism resembles the pH-dependent variation in surface charge of oxide−water interfaces,13 but there is a distinct difference: the surface charge of calcite can also vary depending on the activities of dissolved ions, in particular Ca2+ © 2016 American Chemical Society

and carbonate moieties, as shown by changes in isoelectric point from zeta potential measurements.11,17−21 Interpretation of these data requires understanding the electrical double layer (EDL) structure at the interface where the surface charge density is a main factor. So far, the charge density has been estimated using the number of crystallographically defined functional groups. But, the values varied substantially (from 0.5 to 10 sites/nm2) depending on the physicochemical models chosen in the calculations17,21 and the chemical reactivity of the surface functional groups which can be substantially different from those in solution.22 A direct method for experimentally quantifying the surface charge is to measure the coverage of electrostatically adsorbed counterions.23 Amplitude modulation atomic force microscopy (AFM) was used to image changes in interfacial hydration structure near the (104) plane of single crystal calcite in the presence of dissolved cations (Na+, Rb+, and Ca2+).24 Protuberances in the images were observed near the top oxygen of the carbonate group (close to the location of the water molecules bound to the top oxygen of the carbonate in Figure S1) and were interpreted as adsorbed hydrated cations. However, surface features were distorted because of the presence of the tip itself,25,26 making measurements of the Received: April 29, 2016 Revised: June 17, 2016 Published: June 23, 2016 15216

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values derived from previous electrophoretic experiments21,27 and computational simulations.24,36−38

absolute ion coverage difficult. More recently, synchrotronbased resonant anomalous X-ray reflectivity (RAXR) was applied to determine the coverage and location of Rb+ adsorbed at the calcite (104)−water interface.27 The results identified three species adsorbed from a 10 mM RbCl solution preequilibrated with calcite powder [referred to as “calcitesaturated solution” (CSS) hereafter], with a total adsorbed coverage of ∼0.2 Rb+/AUC (where AUC = 20.2 Å2 is the unit cell area within the (104) plane) or ∼1 Rb+/nm2. The analyses also showed a fourth Rb+ species, which was composed of a periodic series of Rb layers extending away from the surface. Here, we report new measurements designed to determine the effective charge of a “defect-free” calcite surface (i.e., its terrace) by quantifying the maximum coverage of Rb+ adsorbed from CSS. Rubidium was chosen as a probe ion because of its chemical simplicity: adsorption of Rb+ at the calcite−water interface, if it occurs, can be interpreted as driven by electrostatic attraction to satisfy any negative surface charge. In this system, any nonclassical electrostatic interaction (e.g., the ion−ion correlation) is supposed to be negligible,28−30 making the interpretation of the relationship between the adsorbed cation coverage and effective surface charge straightforward. In addition, Rb has an X-ray absorption edge at ∼15.2 keV, favorable for in situ RAXR experiments, which can directly quantify the adsorbed Rb+ coverage at the interface.27,31,32 The experiments were conducted over a range of dissolved Rb+ concentration (0, 1, 10, and 100 mM) to investigate the concentration dependence of Rb+ uptake. For robust control of solution chemistry during the X-ray experiments, all measurements were conducted using an X-ray “transmission cell” (Figure 1) instead of a more commonly used “thin-film cell”

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EXPERIMENTAL SECTION Sample Preparation. Experimental solutions were prepared by dissolving RbCl salt in deionized water (Milli-Q, 18.2 MΩ) followed by an addition of calcite powder to saturate the solution with respect to calcite. A small amount of calcite powder, i.e., about 3 times the mass theoretically required for saturation,39 was used to minimize potential loss of aqueous Rb+ by its sorption, if any, to the surfaces of the added powders. The solutions had been placed on a shaker for ∼10 days for the equilibration with atmospheric CO2, and the CSS aliquots were collected by filtration using a 0.1 μm pore membrane. A single crystal calcite [having 3 × 6 mm2 of area on the (104) plane and 2 mm thick] was cleaved, immediately immersed in a pure CSS solution (i.e., without Rb+) for ∼5 min, and then transferred to an X-ray “transmission cell”. The cell had a solution volume (∼2 mL) sufficiently large to maintain the constant solution composition in contact with calcite even if Rb+ uptake occurred. The number of Rb+ ions in the cell at the lowest RbCl concentration (1 mM) was >10 000 times higher than the number of all surface functional groups of the calcite crystal. The first experiment was conducted in 1 mM RbCl CSS and followed by 10 mM and finally 100 mM solutions. In each step, the sample was reacted with a new solution for ≥15 min prior to the RAXR measurements. Resonant Anomalous X-ray Reflectivity Measurements. In situ RAXR spectra were collected at beamline 33ID-D, Advanced Photon Source. Each spectrum includes a series of X-ray reflectivity signals measured as a function of photon energy (E) near an X-ray absorption edge energy of Rb (K-edge energy, E0 = ∼15.2 keV). The data were obtained at five vertical momentum transfer values in a specular reflection geometry, Q = 0.56, 0.77, 0.97, 2.13, and 2.22 Å−1, where Q = (4π/λ) sin(α) where λ is the X-ray wavelength and α is the angle of the incident X-ray beam with respect to the surface plane. These scattering conditions match those where significant RAXR signals were observed from the previous thin-film cell experiments.27 Specifically, the data collected at the three smallest Q magnitudes are sensitive to the presence of all adsorbed Rb+ species (if any) and therefore are used to estimate the total Rb+ coverage as a function of dissolved Rb concentration. The data at the two largest Q magnitudes are most sensitive to the previously proposed periodically layered Rb structure.27 In addition, the shapes of reflections at Q = 0.97 Å−1, i.e., close to the first midzone of the calcite (104) crystal truncation rod,14 were used to estimate the surface domain size (i.e., the average separation between adjacent steps). The average value was 2.9 ± 0.2 μm, showing that the number density of steps on the surface was extremely low [i.e., less than one step per every 1000 calcite unit cells, AUC0.5/(2.9 × 104)]. These results indicate that our RAXR data were sensitive mostly to the reactivity of the ideal “defect free” (104) plane while any adsorption to the surface defects (e.g., steps and kink sites) was practically invisible to the data. Linear Absorption Correction. The measured RAXR spectra include not only intrinsic contributions from the adsorbed ion distribution but also extrinsic contributions from attenuation of the X-ray beam by solution. The RAXR intensity can be expressed as

Figure 1. Schematic of the setup for RAXR measurements at the calcite (104)−water interface using an X-ray transmission cell.33,34 The cell maintains ∼2 mL of solution in contact with the (104) surface of a calcite crystal (red). The solution is 3 mm thick along the scattering plane defined by incident and reflected X-ray wave vectors, ki and kr, respectively. The momentum transfer vector perpendicular to the surface plane, Q, is defined as kr − ki. X-ray intensity reflected from the surface was measured using an X-ray area detector (PILATUS).40 The inlet and outlet for the solution exchange are indicated using cyan arrows.

(for technical details, see previous studies33,34 and Supporting Information). The obtained RAXR data were analyzed using a model-independent algorithm31 to quantify variations in adsorbed Rb+ coverage as a function of [RbCl], which in turn were fit to a classical uptake isotherm (i.e., Langmuir isotherm) to yield the adsorption strength and maximum ion coverage.35 The obtained thermodynamic constants are discussed in the context of the effective charge of the calcite surface equilibrated with the solution in comparison with the

I(Q , E) ∝ T (Q , E)|FR (Q , E) + FNR (Q )|2 15217

(1)

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Figure 2. Resonant anomalous X-ray reflectivity measured at the calcite (104)−CSS interface containing 1, 10, and 100 mM RbCl (a−c, respectively). Each spectrum is labeled with the Q value where the spectrum was measured. Previously reported spectra obtained in a 10 mM RbCl solution27 using a thin-film cell are shown in (d). The measured intensity is normalized to the nonresonant reflectivity intensity (i.e., intensity calculated without contributions from resonant structure factors), I/INR,31,41 for comparison among the spectra measured at different Q values. All spectra are superimposed with the corresponding solution transmission spectra (T(Q,E); black curve) calculated from the X-ray transmission spectrum measured through the same solution to show the effect of this extrinsic contribution. For the data in (d) the transmission spectra (black dotted lines) are calculated on the basis of the nominal Rb concentration (10 mM) in a solution film that was assumed to be 5 μm thick (i.e., within a range of solution layer thickness developed in a thin-film cell).33 The data are offset vertically for the clarity, as indicated. Measurements were repeated at Q = 2.22 Å−1 for 1 mM RbCl and Q = 2.13 and 2.22 Å−1 for 100 mM RbCl solutions.

where FR and FNR are the resonant and nonresonant structure factors, respectively, and T(Q,E) is the energy (E)- and Qdependent transmission factor of X-rays through the cell.31,33,34 This energy-dependent transmission factor at a fixed Q has a spectral shape that can be similar to an RAXR spectrum, potentially affecting the data analyses. Correcting this effect from the RAXR data measured using a commonly used thinfilm cell can be challenging when the X-ray attenuation is strong, especially when solution layer thickness or ion concentration within the thin film changes with time.34 In contrast, the correction is straightforward for transmission cell experiments where the solution thickness and the ion concentration within the cell are well-defined and stable over time. The absorption correction for a transmission cell geometry can be made directly using a reference X-ray transmission spectrum, Tref(E), measured with the X-ray beam passing through the same solution just above the calcite sample (i.e., the same procedure for X-ray absorption spectroscopy measurement in a transmission mode). For a specular reflection condition where the incident beam angle (α) is the same as the reflected beam angle (β), the transmission factor, T(Q,E) can be expressed as [Tref(E)]1/cos α. The intrinsic RAXR signal then can be obtained as

variations in resonant structure factor amplitude and phase (AR(Q) and ϕR(Q), respectively). Specifically, AR(Q) can be expressed as AR(Q) = ΓRb,tot exp(−Q2⟨uRb⟩2/2) where ΓRb,tot is the total Rb+ coverage (in units of Rb+ per AUC or nm2) and ⟨uRb⟩ is the rms width of the entire Rb+ distribution at the interface.31 When Q is small, the value can be used to estimate the Rb+ coverage adsorbed at the calcite−solution interface.31

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RESULTS AND DISCUSSION RAXR Data. The RAXR data measured in 1, 10, and 100 mM RbCl containing CSS are shown in Figure 2. In a 1 mM RbCl CSS solution (Figure 2a), the spectra show no significant RAXR modulation near E0, indicating that the amount of sorbed Rb+ was small. In 10 and 100 mM RbCl solutions (Figures 2b,c), all spectra exhibit modest modulations, with a decrease in the reflectivity signal above E0 and with modulation magnitudes proportional to the ion concentration. The RAXR data collected in 10 mM RbCl (Figure 2b) appear to be similar to the previous data collected in the same solution composition (Figure 2d). However, these two data sets were measured in two different cell geometries (transmission cell vs thin-film cell, respectively). The comparison of the RAXR data between two data sets requires the consideration of X-ray absorption by the solution above the sample in order to quantify the ion adsorption and therefore to test the reproducibility. The transmission spectrum measured in each solution is superimposed on the RAXR spectra to show contributions of this extrinsic factor (black solid lines in Figure 2). The transmission spectra reproduce almost all features in the RAXR

IRAXR(Q , E) = I(Q , E)/[Tref (E)]1/cos α ∝ |FR (Q , E) + FNR (Q )|2 (2)

The absorption-corrected RAXR signals were analyzed using a model-independent RAXR imaging31 to yield Q-dependent 15218

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Figure 3. Comparison of RAXR at the calcite (104)−CSS containing RbCl after the linear attenuation correction by eq 2. The data collected with 1, 10, and 100 mM RbCl are shown in (a)−(c), respectively. Previously reported spectra obtained in 10 mM RbCl27 using a thin-film cell are shown in (d). Each spectrum is labeled with Q and vertical offset applied for the visual comparison. The spectra derived from the model-independent RAXR analyses are shown in black. Repeated measurements at Q = 2.22 Å−1 for 1 mM RbCl and Q = 2.13 and 2.22 Å−1 for 100 mM RbCl solutions are shown.

spectra, suggesting that these signals originate primarily from Xray absorption by the solution. This result indicates that the contributions from Rb+ adsorbed at the interface (i.e., true RAXR signals) are minor. In contrast, the transmission spectra for the thin-film cell data, calculated with the assumption that the Rb concentration in the solution and the nominal solution layer thickness were unchanged during the course of measurements, essentially have no visible modulation near the E0 (Figure 2d), indicating that the measured RAXR spectra cannot be explained simply by linear absorption of X-rays through the given experimental solution. The true interface-specific RAXR signals (Figure 3) obtained from the measured spectra after the transmission correction using eq 2 are very weak. The small signals, especially for the data measured at low Q, suggest that little (almost no) Rb+ adsorbed to calcite under these conditions.31 The signal magnitudes were quantified using the model-independent RAXR imaging.31 The analyses show that the derived resonant structure factor amplitudes, indicative of the amounts of adsorbed Rb+, were small. In fact, many of them were statistically insignificant at the 95% confident level (Table 1). Langmuir Isotherm Analyses. The resonant structure factor amplitudes at the three lowest Q (0.56, 0.77, and 0.97 Å−1) were used to derive the adsorbed Rb+ coverage in each solution. This coverage corresponds mostly to that of ions that are structurally ordered at the interface, e.g., Stern layer ions including inner-sphere and outer-sphere complexes. It can underestimate the coverage depending on the fractional

Table 1. Resonant Structure Factor Amplitudes (AR) Derived from the Model-Independent Analyses of the RAXR Dataa AR (/nm2) current study

previous study

Q (Å−1)

[Rb] = 1 mM

[Rb] = 10 mM

[Rb] = 100 mM

[Rb] = 10 mM

0.56 0.77 0.97 average: 2.13 2.22

0.04(4) 0.09(7) 0.18(5) 0.10(6) 0.32(24) 0.16(15)b

0.04(4) 0.09(7) 0.18(5) 0.10(5) 0.11(15)b 0.12(10)b

0.12(11) 0.18(7) 0.26(9) 0.18(9) 1.14(41) 0.74(38)

0.84(2) 0.78(3) 0.54(6) 0.72(3) n/a 2.76(8)

a

The numbers in parentheses indicate 1σ uncertainties in the last digits of the parameters. bAveraged over repeated measurements.

contributions from less well ordered species, e.g., ions in a diffuse layer, to which RAXR data are less sensitive. The results show that the amounts of Rb+ adsorbed on the calcite (104) surface were very small and essentially constant over 3 orders of RbCl concentrations (1−100 mM) in CSS. The average adsorbed coverages were ∼0.1 Rb/nm2 in the CSS containing 1 and 10 mM RbCl. It was higher [0.18(9) Rb/nm2, Table 1] for the 100 mM RbCl data, but the increase may not be statistically significant considering its large uncertainty. These observations indicate that either Rb+ adsorption was saturated at [RbCl] ≤ 1 mM (e.g., full compensation of the 15219

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are required to observe the adsorption of Rb+ at the interface. Here, we discuss how these two models can be used to quantify the intrinsic charge of the calcite (104) surface in equilibrium with water. Estimating the Charge of the Calcite (104) Surface. First, we use the thermodynamic parameters derived from the best-fit model to quantify the upper limit to the magnitude in the negative charge of the terrace plane. On the basis of the Γmax value of 0.12 Rb/nm2, we can estimate an effective surface charge of about −0.02 C/m2, which corresponds to the surface potential of −26 mV computed on the basis of the Gouy− Chapman theory.13 Considering that RAXR data are sensitive mostly to specifically adsorbed ions (e.g., ions in the Stern layer),32,35,42 this estimated potential can correspond to the Stern potential (ΨS = −26 mV) (Figure 5). In contrast, the data

surface charge) or the adsorption strength is so weak that almost no adsorption occurred at [RbCl] ≤ 100 mM. The concentration-dependent variation in adsorbed Rb+ coverage was fit to a Langmuir isotherm to explore these two possibilities (Table 2). The results show that the data were best Table 2. Fitting Results of the Adsorbed Rb+ Coveragea model

χ2

ΓMAX

log Kapp Rb

A B

1.4 2.8

0.12(4) 1.0(f)

3.5(11) 0.5(2)

The data were fit to a Langmuir isotherm shape expressed as ΓRb(c) = app ΓMAXcKapp Rb /(1 + cKRb ), where ΓMAX is the maximum surface coverage −1 of Rb, c = [Rb], and Kapp Rb is an apparent adsorption constant (M ). The numbers in parentheses indicate 1σ uncertainties in the last digits of the parameters. a

described by a model indicating a saturated adsorbed coverage of Rb+ for all investigated solution conditions (Figure 4). The

Figure 5. Illustration of the electrical double-layer potential at the calcite (104)−CSS interface.

are less sensitive to ions in a diffuse layer, indicating the need for additional information to fully quantify the surface charge and the potential distribution in the EDL (Figure 5). Zeta potential (ζ) measurements provide an estimate of the net ion charge in the diffuse layer. One difference, however, is that the measurements typically use powder samples that contain a large fraction of defect sites (e.g., steps). As a result, the values derived from the measurements cannot be compared directly to those from our RAXR data, which exclusively probe the reactivity of the terrace of the (104) plane. Therefore, we only compare the magnitudes obtained from two independent measurements to evaluate their relative contributions to the EDL. A previous study showed that the ζ value on calcite was close to zero (+3 mV) measured in calcite saturated solution at pH 8.3 and with pCO2 = 10−3.44 atm. This magnitude is significantly smaller than that of the estimated ΨS (−26 mV), clearly indicating that the contribution from the diffuse profile to the EDL is slight. A similar result was observed at the muscovite (001)−water interface where the RAXR data indicated that ≥90% of the surface charge were compensated by IS and OS Rb+ complexes in the Stern layer,43 leaving only a small portion of charge for compensation above the d plane (Figure 5). Effect of Ca2+. We also consider the possibility that the extremely small affinity for Rb+ to the calcite surface (model B in Table 2) results from the competition from other cations for adsorption to the surface. All experimental solutions were equilibrated with calcite powders and therefore contained dissolved Ca2+. With competition by Ca2+, the apparent adsorption constant (Kapp Rb ) obtained from the model can

Figure 4. Rb coverage (ΓRb) on calcite (104) measured by RAXR. The curves (A and B) are calculated on the basis of two isotherm models shown in Table 2. The gray vertical line shows the RbCl solubility limit at 25 °C.

maximum ion coverage (Γmax) was 0.12(4) Rb/nm2, corresponding to adsorption of only ∼1 Rb+ per every 40 unit cells of the calcite surface. The data were also fit using a model assuming an unsaturated Rb+ coverage. In this model, we used a fixed Γmax = 1 Rb/nm2, the value derived from the best-fit model in the previous study.27 This attempt (determined with a poorer quality of fit) showed a significantly smaller apparent adsorption constant (Kapp Rb ) (Table 2), implying a weaker interaction between the ion and the surface.

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DISCUSSION The RAXR data show that the defect-free calcite (104) surface has a limited affinity for Rb+ uptake. Considering that this adsorption is driven mainly by electrostatic attraction, the small coverage can be interpreted as a consequence of the small magnitude of the effective negative charge of the surface, as indicated by the best-fit isotherm model (Table 2). Alternatively, the data can be explained by a model in which the interaction strength of Rb+ with the calcite surface is extremely weak, and therefore significantly high concentrations 15220

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confirming the unfavorable adsorption of Ca2+ on the (104) terrace.38 No evidence on the formation of OS Ca2+ was found in these studies. In contrast, a more recent simulation conducted for 250 mM CaCl2 showed discrete layering of both Ca2+ and Cl− ions near the interface.24 For Ca2+, the peak density was observed far away from the surface (∼7 Å). Despite this distinct ion layering, the actual enhancement in ion concentration was small. Even for the strongest density peak (spanning 6−8.5 Å), the enhancement was only ∼10% compared to the bulk concentration. This result indicates that the free energy gain for adsorption is also small. For example, ∼10% concentration increase corresponds to ∼0.3 kJ/mol (i.e., 10% of the thermal energy at room temperature) of energy gain for adsorption (corresponding to Kint Ca = ∼1.1). These results indicate intrinsically weak adsorption of Ca2+ to the calcite (104) terrace, implying that the effect of Ca2+ on Rb+ uptake was likely negligible, and therefore the observed small affinity likely resulted from the small magnitude of the negative surface charge. Acidity Limit of Ca on Calcite. Since the charge of the calcite surface originates from changes in the speciation of the (hydrated) surface functional groups, the estimated surface charge (∼0.12 e−/nm2 or 0.02 C/m2) can be used to obtain an insight into the speciation in CSS. The magnitude is small, suggesting that most of the surface groups (about 5 Ca2+− CO32− pairs per nm2 or ∼8.3 μmol/m2) may experience little changes in speciation. On the basis of the surface charge estimated by RAXR, we examine the speciation of the surface Ca2+ of which deprotonation of adsorbed water is considered to be the main source for the negative charge on the terrace.11,17−20,44 The deprotonation reaction can be expressed as

int underestimate the intrinsic adsorption constant (KRb ). 2+ Although the concentrations of Ca (calculated to be between 0.5 and 0.8 mM)39 were smaller than those of Rb+ (1 and 100 mM), the effect can be significant depending on the relative interaction strengths between two cations. The effect of Ca2+ on the adsorption of Rb+ to the surface is estimated using the Langmuir isotherm for two adsorbates. app From the isotherm equation,13 the ratio of Kint Rb to KRb can be expressed as

app int int KRb /KRb = 1 + aCaK Ca

(3)

using the product of the activity and intrinsic adsorption constant for Ca2+ (aCa and Kint Ca, respectively). For all CSS used in our study, the aCa value (∼4 × 10−4, calculated with activity coefficients for Ca2+ ranging from ∼0.8 to ∼0.5)39 was almost constant, so the ratio is controlled primarily by Kint Ca. The results (Figure 6) show that the effect of Ca2+ on Rb+ adsorption is

(≡Ca−H 2O)+1/3 → (≡Ca−OH)−2/3 + H+

(4)

from which the dissociation constant for water bound to the surface Ca ion can be written as

Figure 6. Effect of Ca2+ competition on adsorption of Rb+ to the calcite surface. The ratio of the intrinsic adsorption constant for Rb+ app (Kint Rb) to the apparent adsorption constant (KRb ) is calculated as a function of intrinsic adsorption constant for Ca2+ (Kint Ca). The deviation of that value from 1 indicates the error of the experimental estimation on the adsorption constant of Rb+ caused by Ca2+. The free energy int difference calculated on the basis of Kapp Rb and KRb and the free energy ° ) are also plotted for comparison. of adsorption for Ca2+ (ΔGCa

K a = ([≡Ca−OH][H+]/[≡Ca−H 2O]) exp(ΔZF Ψo/RT ) (5)

where ΔZ is the charge difference between ≡Ca−OH and ≡Ca−H2O functional groups, F is the Faraday constant, Ψo is the surface potential of the calcite (104) plane, R is the gas constant, and T is the temperature.15,45 From eq 5, the pKa value of Ca ions in the calcite terrace can be estimated as

3 mostly negligible when Kint Ca is smaller than ∼10 (corresponding to −17 kJ/mol of the free energy of adsorption for Ca2+, 3 ΔGCa ° ). When Kint Ca ≫ 10 , the calculation shows that the experimental value of Kapp can substantially underestimate Kint Rb Rb. Therefore, the main criteria for determining the significance of the Ca2+ effect is whether the free energy of adsorption for Ca2+ at the interface is larger than this low limit. Previous studies using molecular dynamics simulations24,36−38 show that the free energy of adsorption for Ca2+ to the calcite (104) terrace is significantly smaller than the low limit. A series of simulations conducted under a diluted condition (1 Ca2+ per 360 H2O molecules) identified a distinct IS state for Ca2+ adsorbed to the calcite (104) surface.36 However, the free energy of adsorption was slightly positive 2+ (∼2 kJ/mol corresponding to Kint Ca = ∼0.4) with respect to Ca in the bulk solution, indicating that IS adsorption is not favored thermodynamically. A similar calculation conducted with revised force fields suggests that the free energy difference −5 can be even larger (∼30 kJ/mol corresponding to Kint Ca ≤ 10 ),

pK a = pH − log([≡Ca−OH]/[≡Ca−H 2O]) − 0.434(ΔZF Ψo/RT )

(6)

Using pH = 8.3, [≡Ca−OH]/[≡Ca−H2O] = ∼0.025, ΔZ = −1, F = 9.6485 × 10−2 kJ/(mV mol), Ψo ≈ Ψs = −26 mV, and RT = 2.48 kJ/mol, the pKa for the surface Ca ion is estimated to be ∼9.5. This value likely represents a lower limit for the pKa of the Ca ion in the calcite terrace and, in fact, is very close to the upper limit (10.2) that can be estimated within the precision (i.e., 1 standard deviation) of our RAXR data. Therefore, the actual pKa value can be higher, e.g., similar to the values determined by the surface complexation models.15 Comparison with Previous X-ray Data. Our current RAXR data show significant differences from those in a previous study conducted in a similar system (10 mM RbCl in CSS).27 Specifically, this previous study showed RAXR signals substantially larger than the spectral magnitude expected on the basis of X-ray absorption by the solution (Figure 2). 15221

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The Journal of Physical Chemistry C

structural defects on the overall reactivity of calcite is not a new concept. However, this fact has not been fully incorporated in chemical speciation models mainly because of nontriviality in determining the types, concentrations, and, most critically, equilibrium constants of the individual defects. For the latter, computational simulations can shed light on the dependence of the surface reactivity on the morphology. For example, recent computational studies have shown that most of surface-induced hydrolysis of calcite occurs in the functional groups at steps, i.e., surface species which do not exist on the idealized terrace.15,46 Overall, our experimental results provide a strong constraint on the “maximum” Rb+ adsorption at the calcite (104) surface, which can be used for the development and application of theoretical models for the calcite−water interface system. The results suggest that an explicit distinction in reactivity between idealized terraces vs defect sites needs to be incorporated in descriptions of calcite reactivity.

These apparent differences can be explained partially by a time-dependent increase in the solution ion concentration in a thin-film cell. Time-dependent changes in solution composition within a thin solution film have been documented previously.34 More than 30-fold enhancements in Rb Kα fluorescence yield were observed near the center of a solid surface in contact with a 0.1 mM RbOH solution after 3 h.34 The same trend, albeit with a slower rate (a 10-fold enhancement over ∼6 h, Figure S5), was observed in our repeated measurement using the same thin-film cell used for the previous study. This phenomenon is understood to result partially from the evaporation of water through the Kapton membrane, which leads to an increase in ion concentration within the thin solution layer underneath the membrane.34 With this locally enhanced ion concentration, the energydependent X-ray absorption by the solution can become significant in thin-film cell experiments even when the initial ion concentration is low (e.g., ≤10 mM). For comparison, with a similar enhancement of the ion concentration, e.g., ∼300 mM RbCl instead of 10 mM, the linear absorption by a 5 μm thick solution would result in an about 10% modulation near E0 at Q = 0.56 Å−1 (Figure S6), similar to the size of modulation shown in the spectrum in Figure 2d. This comparison implies that a large part of the RAXR signals observed in the previous study can be explained by energy-dependent linear absorption of Xrays in a solution with locally increased ion concentrations. This increase in local Rb concentration within the solution film can also explain the previously observed RAXR modulation at Q = 2.22 Å−1. This specific scattering condition is close to the (104) Bragg peak of calcite (Q = 2.07 Å−1) where the bulk scattering intensity is strongest. Therefore, it is the condition where the fractional contribution from X-ray scattering signals from the surface, including intensity modulations in RAXR spectra, should be smallest. Our new data measured at Q = 2.13 and 2.22 Å−1 showed much smaller signal amplitudes, most of which were statistically insignificant at the 95% confidence level (Table 1). This irreproducibility of the data indicates that the previously proposed Rb+ adsorption structure, with both adsorbed and layered components, is not intrinsic, and and presumably was an artifact caused by uncontrolled increases in Rb+ concentration in the sample cell. This is supported by the observation that the majority of the previously measured RAXR signals (Figure 2d) can be explained by the linear absorption. However, some of the RAXR spectra, i.e., those at Q = 0.77 and 0.97 Å−1, do not resemble a linear adsorption spectrum. Those features might imply a distinct EDL structure at the calcite (104)−water interface in an elevated RbCl concentration, suggesting a new opportunity for studying the EDL at the calcite−brine interfaces, the results from which can be directly compared with computational studies.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b04364. Experimental details, comparison between X-ray “thinfilm cell” and “transmission cell”, simulated Rb + distribution at the calcite−water interface using linear absorption spectra (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Phone (630)252-6679; fax (630)252-9570; e-mail sslee@anl. gov (S.S.L.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, under Contract DE-AC02-06CH11357 to UChicago Argonne, LLC, as operator of Argonne National Laboratory (for S.S.L., N.C.S., and P.F.) and by the German Ministry for Education and Research (BMBF) through the ImmoRad Project (02NUK019A for F.H.). The reflectivity data were collected at beamlines 13-ID-C (GeoSoilEnviroCARS) and 33-ID-D, Advanced Photon Source. GeoSoilEnviroCARS is supported by NSF-Earth Sciences (EAR-1128799) and DOE-BES-Geosciences (DE-FG02-94ER14466). 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 DE-AC02-06CH11357 to UChicago Argonne, LLC, as operator of Argonne National Laboratory.

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CONCLUSIONS We investigated the adsorption of Rb+ on the calcite (104) surface to quantify the intrinsic charge of the terrace plane in calcite saturated solutions. The results show that the net negative charge is at most 0.12(4) e−/nm2 (corresponding to approximately −0.02 C/m2), extremely small compared to the number of available surface ions (∼2.5% of the total sites). The apparent neutrality of the calcite surface in water indicates that any excess surface charge reported in previous studies does not represent the intrinsic charge of the dominant (104) plane. The results are consistent, however, with the measured charge deriving from defect sites such as steps. The importance of

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REFERENCES

(1) Reeder, R. J. Carbonates - Growth and alteration microstructures. Rev. Miner. 1992, 27, 381−424. (2) Oelkers, E. H.; Gislason, S. R.; Matter, J. Mineral carbonation of CO2. Elements 2008, 4, 333−337. (3) Pokrovsky, O. S.; Golubev, S. V.; Schott, J.; Castillo, A. Calcite, dolomite and magnesite dissolution kinetics in aqueous solutions at acid to circumneutral pH, 25 to 150° C and 1 to 55 atm pCO2: New constraints on CO2 sequestration in sedimentary basins. Chem. Geol. 2009, 265, 20−32. 15222

DOI: 10.1021/acs.jpcc.6b04364 J. Phys. Chem. C 2016, 120, 15216−15223

Article

The Journal of Physical Chemistry C (4) Stipp, S. L.; Hochella, M. F.; Parks, G. A.; Leckie, J. O. Cd2+ uptake by calcite, solid-state diffusion, and the formation of solidsolution - interface processes observed with near-surface sensitive techniques (XPS, LEED, and AES). Geochim. Cosmochim. Acta 1992, 56, 1941−1954. (5) Prieto, M.; Cubillas, P.; Fernandez-Gonzalez, A. Uptake of dissolved Cd by biogenic and abiogenic aragonite: a comparison with sorption onto calcite. Geochim. Cosmochim. Acta 2003, 67, 3859−3869. (6) Chada, V. G. R.; Hausner, D. B.; Strongin, D. R.; Rouff, A. A.; Reeder, R. J. Divalent Cd and Pb uptake on calcite 10(1)4 cleavage faces: An XPS and AFM study. J. Colloid Interface Sci. 2005, 288, 350− 360. (7) Rouff, A. A.; Elzinga, E. J.; Reeder, R. J. The effect of aging and pH on Pb(II) sorption processes at the calcite - water interface. Environ. Sci. Technol. 2006, 40, 1792−1798. (8) Gebrehiwet, T. A.; Redden, G. D.; Fujita, Y.; Beig, M. S.; Smith, R. W. The Effect of the CO32‑ to Ca2+ Ion activity ratio on calcite precipitation kinetics and Sr2+ partitioning. Geochem. Trans. 2012, 13, 1. (9) Callagon, E.; Fenter, P.; Nagy, K. L.; Sturchio, N. C. Incorporation of Pb at the calcite (104)-water interface. Environ. Sci. Technol. 2014, 48, 9263−9269. (10) Sposito, G. Distinguishing adsorption from surface precipitation. ACS Symp. Ser. 1987, 323, 217−228. (11) Stipp, S. L. S. Toward a conceptual model of the calcite surface: Hydration, hydrolysis, and surface potential. Geochim. Cosmochim. Acta 1999, 63, 3121−3131. (12) Zachara, J. M.; Cowan, C. E.; Resch, C. T. Sorption of divalent metals on calcite. Geochim. Cosmochim. Acta 1991, 55, 1549−1562. (13) Stumm, W.; Morgan, J. J. Aquatic Chemistry, 3rd ed.; John Wiley and Sons: New York, 1996. (14) Fenter, P.; Sturchio, N. C. Calcite (104)-water interface structure, revisited. Geochim. Cosmochim. Acta 2012, 97, 58−69. (15) Wolthers, M.; Di Tommaso, D.; Du, Z.; de Leeuw, N. H. Calcite surface structure and reactivity: molecular dynamics simulations and macroscopic surface modelling of the calcite-water interface. Phys. Chem. Chem. Phys. 2012, 14, 15145−15157. (16) Vancappellen, P.; Charlet, L.; Stumm, W.; Wersin, P. A surface complexation model of the carbonate mineral-aqueous solution interface. Geochim. Cosmochim. Acta 1993, 57, 3505−3518. (17) Villegas-Jimenez, A.; Mucci, A.; Pokrovsky, O. S.; Schott, J. Defining reactive sites on hydrated mineral surfaces: Rhombohedral carbonate minerals. Geochim. Cosmochim. Acta 2009, 73, 4326−4345. (18) Somasundaran, P.; Agar, G. E. The zero point of charge of calcite. J. Colloid Interface Sci. 1967, 24, 433−440. (19) Vdovic, N. Electrokinetic behaviour of calcite - the relationship with other calcite properties. Chem. Geol. 2001, 177, 241−248. (20) Moulin, P.; Roques, H. Zeta potential measurement of calcium carbonate. J. Colloid Interface Sci. 2003, 261, 115−126. (21) Heberling, F.; Trainor, T. P.; Lützenkirchen, J.; Eng, P.; Denecke, M. A.; Bosbach, D. Structure and reactivity of the calcitewater interface. J. Colloid Interface Sci. 2011, 354, 843−857. (22) Andersson, M. P.; Rodriguez-Blanco, J. D.; Stipp, S. L. S. Is bicarbonate stable in and on the calcite surface? Geochim. Cosmochim. Acta 2016, 176, 198−205. (23) Sonnefeld, J.; Gobel, A.; Vogelsberger, W. Surface-charge density on spherical silica particles in aqueous alkali chloride solutions. 1. Experimental results. Colloid Polym. Sci. 1995, 273, 926−931. (24) Ricci, M.; Spijker, P.; Stellacci, F.; Molinari, J.-F.; Voïtchovsky, K. Direct visualization of single ions in the Stern layer of calcite. Langmuir 2013, 29, 2207−2216. (25) Ricci, M.; Spijker, P.; Voïtchovsky, K. Water-induced correlation between single ions imaged at the solid-liquid interface. Nat. Commun. 2014, 5, 4400. (26) Voïtchovsky, K. High-resolution AFM in liquid: What about the tip. Nanotechnology 2015, 26, 100501. (27) Heberling, F.; Eng, P.; Denecke, M. A.; Lützenkirchen, J.; Geckeis, H. Electrolyte layering at the calcite(104)−water interface

indicated by Rb+ - and Se(VI) K-edge resonant interface diffraction. Phys. Chem. Chem. Phys. 2014, 16, 12782−12792. (28) Alexander, S.; Chaikin, P. M.; Grant, P.; Morales, G. J.; Pincus, P.; Hone, D. Charge renormalization, osmotic-pressure, and bulk modulus of colloidal crystals - theory. J. Chem. Phys. 1984, 80, 5776− 5781. (29) Shklovskii, B. I. Screening of a macroion by multivalent ions: Correlation-induced inversion of charge. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1999, 60, 5802−5811. (30) Levin, Y. Electrostatic correlations: From plasma to biology. Rep. Prog. Phys. 2002, 65, 1577−1632. (31) Park, C.; Fenter, P. A. Phasing of resonant anomalous X-ray reflectivity spectra and direct Fourier synthesis of element-specific partial structures at buried interfaces. J. Appl. Crystallogr. 2007, 40, 290−301. (32) Lee, S. S.; Fenter, P.; Nagy, K. L.; Sturchio, N. C. Changes in adsorption free energy and speciation during competitive adsorption between monovalent cations at the muscovite (001)-water interface. Geochim. Cosmochim. Acta 2013, 123, 416−426. (33) Fenter, P. A. X-ray reflectivity as a probe of mineral-fluid interfaces: A user guide. In Application of Synchrotron Radiation in LowTemperature Geochemistry and Environmental Science, Reviews in Mineralogy and Geochemistry; Fenter, P. A., Rivers, M. L., Sturchio, N. C., Sutton, S. R., Eds.; Geochemical Society and Mineralogical Society of America: Washington, DC, 2002; Vol. 49, pp 149−220. (34) Lee, S. S.; Fenter, P.; Park, C. Optimizing a flow-through X-ray transmission cell for studies of temporal and spatial variations of ion distributions at mineral-water interfaces. J. Synchrotron Radiat. 2013, 20, 125−136. (35) Park, C.; Fenter, P. A.; Sturchio, N. C.; Nagy, K. L. Thermodynamics, interfacial structure, and pH hysteresis of Rb+ and Sr2+ adsorption at the muscovite (001)-solution interface. Langmuir 2008, 24, 13993−14004. (36) Kerisit, S.; Parker, S. C. Free energy of adsorption of water and metal ions on the {10−14} calcite surface. J. Am. Chem. Soc. 2004, 126, 10152−10161. (37) Tribello, G. A.; Bruneval, F.; Liew, C.; Parrinello, M. A molecular dynamics study of the early stages of calcium carbonate growth. J. Phys. Chem. B 2009, 113, 11680−11687. (38) Raiteri, P.; Gale, J. D.; Quigley, D.; Rodger, P. M. Derivation of an accurate force-field for simulating the growth of calcium carbonate from aqueous solution: A new model for the calcite-water interface. J. Phys. Chem. C 2010, 114, 5997−6010. (39) Bethke, C. M.; Yeakel, S. The geochemist’s workbench: Reference manual. In Aqueous Solutions, LLC: Champaign, 2013. (40) Eikenberry, E. F.; Bronnimann, C.; Hulsen, G.; Toyokawa, H.; Horisberger, R.; Schmitt, B.; Schulze-Briese, C.; Tomizaki, T. PILATUS: a two-dimensional X-ray detector for macromolecular crystallography. Nucl. Instrum. Methods Phys. Res., Sect. A 2003, 501, 260−266. (41) Lee, S. S.; Nagy, K. L.; Park, C.; Fenter, P. Enhanced uptake and modified distribution of mercury(II) by fulvic acid on the muscovite (001) surface. Environ. Sci. Technol. 2009, 43, 5295−5300. (42) Lee, S. S.; Fenter, P.; Park, C.; Sturchio, N. C.; Nagy, K. L. Hydrated cation speciation at the muscovite (001)-water interface. Langmuir 2010, 26, 16647−16651. (43) Lee, S. S.; Fenter, P.; Nagy, K. L.; Sturchio, N. C. Monovalent ion adsorption at the muscovite (001) - solution interface: Relationships among ion coverage and speciation, interfacial water structure, and substrate relaxation. Langmuir 2012, 28, 8637−8650. (44) Heberling, F.; Bosbach, D.; Eckhardt, J. D.; Fischer, U.; Glowacky, J.; Haist, M.; Kramar, U.; Loos, S.; Muller, H. S.; Neumann, T.; et al. Reactivity of the calcite-water-interface, from molecular scale processes to geochemical engineering. Appl. Geochem. 2014, 45, 158− 190. (45) Dzombak, D. A.; Morel, F. M. M. Surface Complexation Modeling: Hydrous Ferric Oxide; Wiley: Hoboken, NJ, 1990; p 416. (46) Andersson, M. P.; Stipp, S. L. S. How acidic is water on calcite? J. Phys. Chem. C 2012, 116, 18779−18787. 15223

DOI: 10.1021/acs.jpcc.6b04364 J. Phys. Chem. C 2016, 120, 15216−15223