Ion Exchange Thermodynamics at the Rutile–Water Interface: Flow

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Ion Exchange Thermodynamics at the Rutile−Water Interface: Flow Microcalorimetric Measurements and Surface Complexation Modeling of Na−K−Rb−Cl−NO3 Adsorption Tyler Hawkins,† Nicholas Allen,† Michael L. Machesky,‡ David J. Wesolowski,§ and Nadine Kabengi*,†,∥ †

Department of Geosciences, Georgia State University, Atlanta, Georgia 30303, United States Illinois State Natural History Survey, Prairie Research Institute, Champaign, Illinois 61820, United States § Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ∥ Department of Chemistry, Georgia State University, Atlanta, Georgia 30303, United States ‡

S Supporting Information *

ABSTRACT: Flow microcalorimetry was used to investigate the energetics associated with Rb+, K+, Na+, Cl−, and NO3− exchange at the rutile−water interface. Heats of exchange reflected differences in bulk hydration/dehydration enthalpies (Na+ > K+ > Rb+, and Cl− > NO3−) such that exchanging Na+ or Cl− from the surface was exothermic, reflecting their greater bulk hydration enthalpies. Exchange heats were measured at pH 2, 3.25, 5.8, and 11 and exhibited considerable differences as well as pH dependence. These trends were rationalized with the aid of a molecularly constrained surface complexation model (SCM) that incorporated the inner-sphere binding observed for the cations on the rutile (110) surface. Explicitly accounting for the inner-sphere binding configuration differences between Rb+, K+, and Na+, as well as accompanying differences in negative surface charge development, resulted in much better agreement with measured exchange ratios than by considering bulk hydration enthalpies alone. The observation that calculated exchange ratios agreed with those measured experimentally lends additional credence to the SCM. Consequently, flow microcalorimetry and surface complexation modeling are a useful complement of techniques for probing the energetics associated with ion exchange and adsorption processes and should also serve to help validate molecular simulations of interfacial energetics.

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INTRODUCTION The rutile−water interface has been the subject of numerous investigations and in particular the predominant (110) surface, which has been studied in an unprecedented level of detail with both experimental and computational approaches, separately and in combination.1−6 Consequently, a great deal of molecular-level understanding has been attained, and this has led to a firmer scaffolding for interpreting familiar macroscopic phenomena such as surface charge development,7−9 ion adsorption processes,10−12 and electrokinetic behavior.13,14 However, conspicuously missing from studies of the rutileaqueous solution interface (as well as many other metal oxide interfaces) are direct measurements of the energies of ion sorption and exchange. The literature on energetics and enthalpies of exchange, adsorption, and surface protonation reactions, especially those directly supported by experimental data, remains scarce despite their fundamental nature.15−17 Thermodynamic parameters of metal oxide−aqueous solution interfacial reactions have been traditionally determined from sorption isotherms. Obtaining sorption isotherms at different temperatures provides data for deriving the adsorption enthalpies (ΔH°ads) from the Clausius−Clayperon equation.18 Alternatively, knowledge of adsorption equilibrium constants at © XXXX American Chemical Society

two or more different temperatures can be used to determine ΔH°ads from the van’t Hoff or more complicated expressions involving heat capacity terms.19,20 Direct measurement of surface reaction heats has been made possible through calorimetry, which in both flow-adsorption and titration mode, such as isothermal (the energy needed to maintain a constant temperature is measured) and isoperibol (the temperature variation of sample is measured, while the temperature of the surrounding environment is maintained constant) titration calorimetry, has provided an excellent adjunct to isotherm-derived thermodynamic quantities.21,22 For rutile surface studies, isoperibol titration calorimetry has been successfully used to measure protonation enthalpies that were reported to be exothermic and about −20 kJ/mol near the pHzpc.16,23 The temperature compensated MUSIC model of Machesky et al.7 also yields intrinsic protonation enthalpies of −20 to −25 kJ/mol for rutile. Flow adsorption microcalorimetry (FAMC) has also been used to measure sorption and exchange enthalpies for a number of ions on various oxide Received: March 14, 2017 Revised: April 28, 2017 Published: May 1, 2017 A

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Langmuir surfaces,24−26 but no measurements have been reported thus far on rutile. Heats measured via calorimetry can be difficult to interpret because they reflect the sum total of all contributing reactions. For surface ion exchange reactions, this includes the enthalpy of dehydration of sorbing inner-sphere ions, the rehydration of the leaving ions, and any changes in surface protonation and/or interfacial water restructuring or binding that involve energy changes. Depending on the calorimetric method, these reactions can also include heats associated with mixing, dilution, dissolution/precipitation, as well as those of the ion binding reactions of interest. Moreover, the ion binding reactions themselves often vary with important variables such as pH, ionic strength and composition, and surface coverage. There is mounting evidence that exchange enthalpies are strongly related to the dehydration/rehydration of ions adsorbing/ desorbing at the surface,27−29 and hydration-related parameters have been used to rationalize experimental observations,30 although other cation specific properties and substrate properties, such as charge density, polarizability, and basicity are also known to be important.31 Consequently, quantitative partitioning and interpretation of measured heats can benefit greatly from the use of surface complexation models (SCMs) that describe the interfacial distribution of adsorbed species through equilibrium constant expressions that incorporate electrostatic effects.32 Here we seek to interpret microcalorimetric measurements of Rb+, K+, and Na+ exchange enthalpies on rutile using a stateof-the-art SCM framework (CD-MUSIC) that has also been constrained using a variety of molecular-scale information including synchrotron-based X-ray scattering, as well classical molecular dynamics and ab initio modeling techniques.9 It is important to note that these cations are commonly considered to interact nonspecifically with oxide surfaces, and are typical components of background ionic strength buffers (e.g., NaCl, KNO3). However, at least on rutile they adsorb in the same specific inner-sphere binding configurations as do multivalent cations such as Sr2+and Y3+, although outersphere binding also occurs, particularly at near-neutral charge conditions.6 To our knowledge, this is the first attempt to rationalize flow calorimetry data with the aid of an SCM. It will be shown that this leads to a more complete understanding of those data, and hence should serve as an approach for interpreting similar calorimetric studies in the future, as well as a powerful aid for validating molecular simulations of interfacial energetics.

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To obtain the thermal signatures and subsequently the heats of ion exchange (Qexch, in mJ/mgsolid), a known mass of rutile (approximately 40 mg) was homogeneously packed into the sample holder. After equilibration with an initial solution (Sol1), for example, 0.05 M NaCl, until a steady thermal baseline was achieved, the input solution was switched to another solution (Sol2) differing only by the cation, that is, KCl, at the same concentration and pH. The heat of exchange generated from the displacement of an interfacially bound cation by another cation, for example, the displacement of Na+ by K+, was recorded. Blank experiments without the sorbing solid phase present demonstrated that solution mixing alone does not contribute significanly to the observed ion exchange heats. Once the signal returned to baseline indicating the exchange reaction had ended, the input solution was reverted to Sol1 and the peak produced from the heat of the reverse cation displacement reaction was recorded. Several replicates (∼4−10) of ion exchange in each direction, Sol1 to Sol2 and Sol2 to Sol1, were recorded before moving to a different cation pair. The solution pH was adjusted to 2.0 ± 0.01 and 3.25 ± 0.01 with 5 M HCl for NaCl, KCl, and RbCl solutions and with 5 M HNO3 for NaNO3 solutions. Correspondingly, the solution pH was adjusted to 11.0 ± 0.1 with 5 M NaOH for NaCl and NaNO3 solutions, 5 M KOH for KCl solutions, and 5 M RbOH for RbCl solutions. No strong acid or base adjustments were necessary for the pH 5.8 ± 0.1 solutions (airsaturated pH of deionized water). Changes in ionic strength resulting from pH adjustments were determined to be less than ≤1%. It is important to note that before each pH change, the sample surface was flushed at the new pH value for 3 days to ensure the surface was indeed equilibrated at the target pH before beginning the collection of exchange cycle data. The pH of the influent and effluent solutions was monitored to ensure it remained consistent. The solubility of rutile under all solution conditions is very low even at pH 2 where equilibrium solubility is less than 0.1 μM.38 Furthermore, the calorimeter is equipped with a carbonate trap consisting of a 12 N NaOH solution to avoid further contact of atmospheric CO2 with the solutions. Surface Complexation Modeling. Tioxide rutile surface charge titrations were conducted at 25 °C in 0.03 and 0.3 m NaCl, RbCl, and KCl using a glass electrode autotitrator system according to procedures given in Ridley et al.34 The resulting surface charge data were then fit with a molecularly constrained SCM9 based on the CDMUSIC framework of Hiemstra and Van Riemsdijk39 to determine intrinsic binding constants for the various adsorption geometries observed, as well surface site distributions with respect to pH. The SCM from Machesky et al.9 was only fit to NaCl and RbCl data and only at 0.03 and 0.3 m ionic strength. Thus, two extensions of the SCM were necessary to generate results fully compatible with the flow microcalorimetry data. First, the 0.03 and 0.30 m KCl titration data from Ridley et al.35 were refit with the SCM of Machesky et al.9 Only the two intrinsic binding constants describing the inner-sphere binding of K+ were varied during the fitting process. The 0.03 and 0.3 m surface charge titration data and model fits, along with the pertinent model equations, and resulting model parameters for Rb+, K+, and Na+ are given in Figure S3 and Table S1, respectively. Second, from the 0.03 and 0.3 m surface charge titration data fits, 0.05 m surface charge data, and Rb+, K+, and Na+ binding site distributions were simulated for direct comparison with the calorimetric results. The simulated 0.05 m surface charge data are given in Figure 1.

EXPERIMENTAL SECTION

Solid and Solutions. The rutile sample used in this study was obtained from Tioxide Specialties Ltd. (Cleveland, U.K.) and has been used and described extensively in previous studies.33,34 Briefly, before being used the sample was subjected to hydrothermal pretreatment following Machesky et al.33 The specific N2-BET surface area was found to be 17.0 ± 2 m2/g, consistent with previous measurements on the same sample.35 Scanning electron microscopy analysis revealed needle-shaped particles, approximately 500 nm long and 50 nm wide (Figure S1), with the (110) surface plane dominant. All solutions were prepared from ACS reagent grade chemicals, 18.2 MΩ deionized water, and at a concentration of 0.05 M. Flow Microcalorimetry Experiments. The flow adsorption microcalorimeter (FAMC) used in this study was custom-designed and fabricated in the Kabengi laboratory at Georgia State University. A description of the instrumentation and basic operational procedures of the FAMC have been detailed previously36,37 and are summarized in Section 2 of the SI.

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RESULTS AND DISCUSSION Calorimetric Trends. The heats of exchange for Na+ and K+, Na+ and Rb+, as well as Rb+ and K+ were measured using the procedure described above at pH values of 2.0, 3.25, 5.8 and 11.0, and with all solutions at 0.05 M concentration. Additionally, the heats of Cl− and NO3− exchange were measured using the procedure described above using 0.05 M NaNO3 and NaCl solutions. Table 1 lists the ion exchange pair experiments conducted, their compositions and pH values, their abbreviations that are used in the subsequent text, and the sign B

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of the calorimetric signal measured. It is immediately clear in Table 1 that all experiments where an ion with a smaller bare ionic radius is displaced by an ion with a larger radius resulted in an exothermic response, while displacement of larger ions by smaller ones invariably resulted in endothermic responses (bare ionic radii: Na+ = 102 pm < K+ = 138 pm < Rb+ = 149 pm and Cl− = 181 pm < NO3− = 200 pm, radii from Marcus;40 values presented in Table S2). Figure 2 shows representative raw data (calorimetric signal versus time) for [K/Na] and [Na/K] exchange that were obtained at pH 2.0, 3.25, 5.8, and 11, and for [Rb/Na] and [Na/Rb] exchange at pH 5.8 and 11.0. Those for [Cl/N] and [N/Cl] at all four pHs and for [Rb/K] and [K/Rb] at pH 5.8 are presented in Figures S4 and S5, respectively. Both K+ and Rb+ replacing Na+ was exothermic, while Na+ replacing either K+ or Rb+ was endothermic. The heat of exchange reflects the net summation of several reactions, a principal one being the difference between the partial dehydration of the incoming exchanging species (an endothermic process), and rehydration of the desorbed exchanged species, which is an exothermic process.41 For example, the [Na/K] exchange includes the exothermic rehydration of Na+ as it leaves the surface and enters the bulk solution and the endothermic dehydration of K+ as it adsorbs on the surface as an inner-sphere species. From our previous experimental and molecular dynamics simulation results,9,42 we know that Na+ and Rb+ adsorb predominantly as inner-sphere species at negatively charged rutile surfaces, and we infer K+ does as well. Likewise, Cl− adsorbs in inner-sphere fashion on positively charged rutile surfaces.9 Thus, the net exothermic heat of exchange (Qexch) can be broadly understood as reflecting the larger bulk hydration enthalpy (ΔHhyd) of Na+ (−416 kJ/mol) compared to the smaller (in absolute magnitude) bulk dehydration enthalpy of K+ (+334 kJ/mol). Conversely, the net Qexch for the reverse [K/Na] reaction is endothermic (bulk ΔHhyd data, along with other ion-specific properties are compiled in Table S2). To our knowledge, there are no other reported directly measured heats of exchange for Rb+, K+, or Na+ on rutile. However, the exothermicity of the [Na/K] exchange and the

Figure 1. Simulated surface charge for the rutile in 0.05 M RbCl, KCl and NaCl. The dotted lines intersect at the pHznpc (pH = 5.4, surface charge = 0).

Table 1. Ion Exchange Pairs Included in the Microcalorimetric Studies exchange Pairs [Y/X]a Y

X

abbreviation

NO3− Cl− K+ Na+ Rb+ Na+ Rb+ K+

Cl− NO3− Na+ K+ Na+ Rb+ K+ Rb+

[N/Cl] [Cl/N] [K/Na] [Na/K] [Rb/Na] [Na/Rb] [Rb/K] [K/Rb]

solution pHs includedb,c

sign of calorimetric signal

2.0; 3.25; 5.8; 11.0

(+) endothermic (−) exothermic (+) endothermic (−) exothermic (+) endothermic (−) exothermic (+) endothermic (−) exothermic

2.0; 3.25; 5.8; 11.0 5.8; 11.0 5.8

a

Y/X, the exchange of ion Y by ion X. bAll solutions were at a concentration of 0.05 M. cThe designation of the pH as a treatment variable throughout the text omits the standard errors associated with the adjustment for convenience.

Figure 2. Raw calorimetric signals for [Na/K] and [K/Na] exchange obtained at pH values of 2.0, 3.25, 5.8, and 11.0 (left), and [Na/Rb] and [Rb/ Na] exchange at pH values of 5.8 and 11.0 (right). Inset gives [Na/K] and [K/Na] exchange at pH values of 2.0 and 3.25 in expanded fashion. An increase in voltage resulting in positive peaks corresponds to a release of energy and hence exothermic reactions. A decrease in voltage and hence negative peaks indicates endothermic reactions. C

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Langmuir Table 2. Summary of Heat of Exchange Values Corresponding to the Ion Exchange Pair Experimentsa Qexchd (mJ/mgsolid)

exchange pair [Y/X]b pH

c

[K/Na] [Na/K] [N/Cl] [Cl/N] [Rb/Na] [Na/Rb] [Rb/K] [K/Rb]

2.0 0.015 −0.032 0.083 −0.066

(0.001) (0.002) (0.001) (0.002) f f f f

3.25 e

0.020 −0.040 0.066 −0.068

(0.001) (0.002) (0.002) (0.001) f f f f

5.8 0.042 −0.062 0.042 −0.056 0.071 −0.106 0.035 −0.039

(0.0004) (0.001) (0.003) (0.002) (0.005) (0.009) (0.003) (0.002)

11.0 0.262 −0.340 0.022 −0.022 0.144 −0.251

(0.011) (0.005) (0.001) (0.001) (0.001) (0.008) f f

a

A negative value indicates an exothermic reaction. bY/X, the exchange of ion Y by ion X. cAll solutions were at a concentration of 0.05 M. Negative values correspond to an exothermic reaction. eNumbers in parentheses corresponds to ± one standard deviation of all replicates. fNot measured. d

calorimetric Qexch values obtained for an amorphous aluminum hydroxide were proportional to the magnitude of the surface charge, and they were able to extrapolate, albeit absent a priori adoption of any specific SCM, an apparent zero point of net charge (ZPNCapp) of 9.4 that matched literature pHznpc values.45,46 Partitioning of Qexch Based on SCM. The thermal signatures in Figure 2 (and Figures S4 and S5) are highly reproducible in that for a specific exchange both the shape and size of the signatures were the same over all the replicates that were conducted, irrespective of the order in which the experiments were performed. Both the [K/Na], [Rb/Na], and [N/Cl] endotherms and the [Na/K], [Na/Rb], and [Cl/ N] exotherms returned to baseline in similar amounts of time, indicating the ion-exchange reactions are reversible, as expected. The integrated peak areas, however, did not always match, as evident visually in Figure 2 and numerically in Table 2. [K/Na] and [Na/K] presented a systematic asymmetry wherein the [Na/K] exothermic exchange was significantly bigger than the corresponding [K/Na] endotherm by 53%, 50%, 32%, and 23% as pH increased from 2.0, to 3.25, to 5.8, and to 11.0, respectively. Similarly, [Na/Rb] exotherms were larger than corresponding [Na/Rb] endotherms by 33% and 43% at pHs 5.8 and 11.0, respectively. [K/Rb] and [Rb/K] exotherms and endotherms were nearly identical in size. [Cl/ N] and [N/Cl] did not present a systematic trend and were identical in size at pH values of 3.25 and 11.0 but different at 2.0 and 5.8. Rutile surface charge becomes increasing negative above the pHznpc in the order RbCl < KCl < NaCl (Figure 1). This trend is characteristic of negative surface charge development on rutile1,35 and is due to adsorbed amounts increasing in the order Rb+ < K+ < Na+ for solutions of the same salt concentration and pH. Adsorbed amounts can be quantified with our SCM (Table S3) and a comparison of these amounts with [K/Na], [Na/K], [Rb/Na], and [Na/Rb] Qexch values are given in Figure 4. Absolute Qexch values for [Na/K] and [Na/ Rb] exchange are greater than those for [K/Na] and [Rb/Na] exchange and more Na+ than K+ and Rb+ is adsorbed at those same pH values. Therefore, Qexch for [Na/K] and [Na/Rb] are greater because more Na+ is released (and rehydrated) when exchanged by K+ or Rb+ at a given pH value then when K+ or Rb+ are exchanged by Na+. Although Qexch values were only determined at a few pH values, it is apparent that the correspondence between amounts adsorbed and Qexch values are not perfect (i.e, 1:1). However, total amounts adsorbed do not account for binding configuration differences and hence

endothermicity of the corresponding [Na/K] exchange agrees with previously reported results obtained with flow microcalorimetry on an amorphous aluminum hydroxide25,43 and on a Utlisol.36 Relationship Between Qexch and Surface Charge. The Qexch values (mJ/mgsolid) determined from integrating the calorimetric signals depicted in Figure 2 are given in Table 2. As is also apparent in Figure 2 (and Figure S4), cation exchange heats increase in absolute magnitude with increasing pH, while anion exchange heats increase in absolute magnitude with decreasing pH. These calorimetric trends mirror the surface charge behavior of rutile (Figure 1), which becomes more negative above and more positive below the point of zero net proton charge (pHznpc) of 5.4.33 This correspondence is shown in Figure 3 where the Qexch for [K/Na], and [N/Cl], as

Figure 3. Heats of exchange for [K/Na] (circles) and [N/Cl] (squares) exchange, along with the simulated 0.05 M surface charge relative to pH values for NaCl (triangles). The dotted lines connecting the heat of exchange values are to aid the eye.

well as the simulated 0.05 M NaCl surface charge results are plotted relative to pH. This plot clearly indicates small but nonzero exchange enthalpies for cations at pHs far below the pHpzc and for anions at pHs far above the pHpzc. It is also evident that the cation and anion exchange heats nearly compensate each other at pH 5.8, which is also near the experimentally determined pHznpc of 5.4. This is to be expected because cation and anion binding is compensatory near the pHznpc.44 Kabengi et al.25 have previously shown that D

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For Rb+, inner-sphere binding is predominately tetradentate (TD), that is, to two terminal oxygen groups (TO) and two bridging oxygen groups (BO), which populate the rutile (110) surface in a 1:1 ratio.47 In the process of forming this TD complex, four primary hydration sphere waters are lost and are replaced by the TO and BO groups. In addition, there is a minor bidentate (BD) inner-sphere complex in which Rb+ is bound to one TO and one BO group (BOTO), which requires the loss of two primary hydration sphere waters, and finally an outer-sphere (OS) Rb+ species in which the primary hydration sphere remains intact. The distribution of surface sites between pH 2 and 11.5 for the rutile (110) surface in 0.05 M RbCl solution is given in Figure 5 and the dominance of the TD Rb+ complex above the pHznpc of 5.4 is apparent. Figure 4. Measured heats of exchange (absolute values, open symbols and lines) and the corresponding total amounts of Na+, K+, Rb+, and Cl− adsorbed (closed symbols and lines) as quantified by the surface complexation model relative to pH.

relative amounts of hydration/dehydration accompanying the exchange process. Hydration/Rehydration Effects. Heat effects resulting from hydration/dehydration differences can be quantified with the SCM. As mentioned above, a primary contributor to observed Qexch values is the dehydration/rehydration of the adsorbing/ desorbing ions during the exchange process. Therefore, for a given exchange pair the ratios of the bulk ΔHhyd should be similar to the ratios of the Qexch measured calorimetrically, defined for a particular set of exchange pairs as the ratio of the less energetic exchange to the more energetic exchange, taken in absolute value. These bulk ΔHhyd ratios for the cation exchange pairs investigated in this study are given in Table 3,

Figure 5. Distribution of terminal oxygen (TO) and bridging oxygen (BO) groups in 0.05 M RbCl between pH 2 and 11.5. The inset shows site fractions from 0 to 0.01 in expanded fashion. TOH(−) and BO(−) are negatively charged terminal and bridging oxygens, respectively, and TOH2(+) and BOH(+) the positively charged counterparts. Outer-sphere Rb+ species to TO and BO groups are in blue, the bidendate BOTO species in dark yellow, the tetradentate (TD) species in dark green, and the inner-sphere Cl complex to a BOH group (ClBOH) in orange.

Table 3. Calculated Ratios for [Rb/K], [Rb/Na], and [K/ Na] Exchange from the Measured Heats of Exchange (Qexch) at pH 5.8 (2nd column), 11 (3rd column), and bulk hydration enthalpies (ΔHhyd, 4th column)a Qexch ratio [Y/ X]/[X/Y]b exchange pair [Y/X]

pH 5.8

Rb/K Rb/Na K/Na

0.90 0.67 0.67

SCM ratio

SCM-SC ratio

pH 11

ΔHbulk ratio

pH 5.8

pH 11

pH 5.8

pH 11

0.57 0.77

0.91 0.74 0.80

0.95 0.66 0.69

0.86 0.72 0.83

0.92 0.59 0.64

0.79 0.60 0.76

The surface site speciation in the presence of 0.05 M NaCl between pH 2 and 11.5 is given in Figure S6. Inner-sphere binding is more complex and is dominated by a bidentate BOTO complex (requiring the loss of two primary hydration sphere water molecules) above the pHznpc. An inner-sphere TD complex is also prominent and becomes more so with increasing pH. Finally, there are minor amounts of bidentate TOTO and OS complexes. Figure S7 presents the presumed surface site speciation for 0.05 M KCl. Although there is no direct molecular-scale information on which to base K+ binding at the rutile (110) surface, it is probably very similar to that of Rb+, given their similar size and hydration properties (Table S2). Thus, innersphere binding is most likely predominately TD. The binding site distributions can be used to more precisely estimate enthalpic effects due to dehydration/rehydration. For example, as pH increases above the pHznpc, more Na+ moves from the BD BOTO to the TD configuration (Figure S6). However, for Rb + (and most likely K+) TD binding predominates under all negative surface charge conditions due to its lower dehydration energy. Thus, because Na+ and Rb+ converge toward similar configurations with increasing pH,

a

SCM ratios are bulk hydration enthalpy ratios corrected for cationspecific dehydration at pH 5.8 (5th column), and 11 (6th column) as calculated from the SCM. SCM−SC ratios are SCM ratios further corrected for cation specific surface charge differences at pH 5.8 (7th column) and 11 (8th column). bRatio of the less energetic exchange to the more energetic exchange, taken in absolute value.

along with the corresponding Qexch ratios at pH 5.8 and 11. The ΔHhyd and Qexch ratios for Rb/K are nearly identical, although the Qexch ratio was only determined at pH 5.8. However, the ΔHhyd and Qexch ratios for the Rb/Na and K/Na pairs are less similar. Moreover, those Qexch ratios vary with pH (although in opposite directions), while the ΔHhyd ratios are by definition invariant with pH. Rb+, K+, and Na+ bind to the rutile surface in different inner-sphere configurations requiring different amounts of waters lost, depending pH and charge and these differences are captured by the SCM. E

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negatively charged at pH 2.0, and 15% of the TO groups are positively charged at pH 11. Moreover, our SCM predicts that a small proportion (