The Variable Capacitance Model - American Chemical Society

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The Variable Capacitance Model: A Strategy for Treating Contrasting Charge-Neutralizing Capabilities of Counterions at the Mineral/ Water Interface Jean-François Boily* Department of Chemistry Umeå University SE-901 87 Umeå Sweden S Supporting Information *

ABSTRACT: Thermodynamic models predicting ion adsorption at mineral/water interfaces can have limitations from the simplifying assumptions that compact plane thicknesses and capacitance values are constant, and that charge densities of electrolyte counterions of different charge-to-size ratios lie at the same planes of adsorption, or split between different planes. To address these limitations a thermodynamic adsorption modeling framework was developed to account for coexisting compact planes for each type of counterion complexes formed on a single mineral surface. This framework was developed to predict charge development at lepidocrocite (γ-FeOOH) particle surfaces suspended in aqueous solutions of NaCl and NaClO4. The model incorporates properties of Cl−, ClO4−, and Na+ complexes formed at the (001) and (010) faces of this mineral obtained by molecular dynamics (MD) simulations. This concept was incorporated in a thermodynamic adsorption model that predicts an overall variable compact plane capacitance in terms of a linear combination of the capacitances of ion-specific EDL structures scaled for their relative surface loadings. These capacitance values are in turn constrained by compact plane thicknesses of every Cl−, ClO4−, and Na+ complex, based on their MD-derived structures and atomic densities. The model predicts experimental potential-determining (H+, OH−) data for submicrometer-sized synthetic lepidocrocite particles exhibiting both (001) and (010) faces. It also isolates electrostatic contributions from these faces. A computer code solving for this Variable Capacitance ModelVCMis provided in the Supporting Information section of this article, and can be readily modified to predict molecular-level details of any other mineral/water interface systems using this methodology.

1. INTRODUCTION Electrolyte counterions are key species driving charge development at mineral/water interfaces.1−7 Thermodynamic adsorption modeling frameworks coupled to electric double layer (EDL) models are commonly used to predict the interplay between potential-determining ions (p.d.i.; H+, OH−) and electrolyte ion loadings.8−11 Most treat mineral/water interfaces as molecular capacitors of constant capacitance value by allocating charges of p.d.i. and electrolyte ions at generic adsorption planes separated by a charge-free space (Figure 1). In this framework, a surface’s ability to store charge is related to the capacitance of the compact (e.g., Stern or inner-Helmholtz) layer. This term is, in turn, related to the thickness of the compact layer, ideally defined by the thickness of layer(s) of intervening water molecules and the distance of closest approach of electrolyte counterions. More recent experimental12−15 and theoretical14,16−18 studies are, however, underscoring the interdependent nature of mineral/water interface structure in relation to electrolyte counterion hydration state and coordination geometries. An increasing body of literature12,17,18 is, moreover, revealing patch-wise distributions of such species on a single mineral surface, each with their inherently distinct local structures and charge densities, and therefore charge-storing capacities. There is consequently a need for improving modeling strategies predicting such © 2014 American Chemical Society

molecular-level information at mineral/water interfaces.2−4,12,18,19 Well-known current-day strategies predicting mineral surface charge-neutralizing capabilities of electrolyte ions include, among others, multiplane EDL5,20,21 and charge distribution (CD)22 models (Figure 1). Multiplane EDL models assign charges of every type of counterion to distinct adsorption planes as a means to express an ion’s specific chargeneutralizing capability. CD modeling distributes, in turn, fractional charges of polyatomic23,24 and even monatomic25,26 adsorbates between a more limited number of adsorption planes to account for such differences, as well as to convey notions of coordination geometries into models. Compartmentalization of partial atomic charges can, however, raise concerns when recalling that electron densities tend to be continuously distributed within species, and thus not necessarily discretely localized toward their coordinating ligands or hydration sheaths.27 While these and many other models do provide insightful means at predicting interfacial processes, none truly account for ion-specific patch-wise distributions taking place on a single surface. None can therefore fully account for variations Received: October 11, 2013 Revised: January 18, 2014 Published: January 30, 2014 2009

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Figure 1. Schematic representations of EDL structures from the literature: Three Plane Model22 (TPM), Multiple Plane Model20,21 (MPM), Charge Distribution-Three plane Model22 (CD-TPM), and Smit Model (SMIT).30

Figure 2. Lepidocrocite particles under study. (a) Idealized representation of the morphology. (b) High resolution transmission electron microscopy of synthetic particles collected on a JEOL JEM-2100 microscope with a LaB6 filament. The images show diffraction fringes running parallel to the ⟨100⟩ crystallographic direction. The particles are bound by the (010) and (001) planes, as confirmed by selected area electron diffraction (not shown). Particles tend to aggregate, and even form mesocrystals, through the (010) plane, explaining the seemingly large particle widths in the image. They disaggregate in aqueous media. (c) Molecular structure of lepidocrocite and of its hydroxo group population at (010) and (001) planes.

synthetic lepidocrocite particles is also motivated by the contrasting structures and charging behaviors of the dominant (001) and (010) faces (Figure 2), thus forcing the incorporation of different types of interfacial species and contrasting electrostatic potentials between different crystallographic faces within a single model. Under ambient conditions, the (001) face is ideally terminated by an equal mixture of −OH (Fe−OH), μ-OH (Fe2−OH) and μ3-OH ( Fe3OH) groups.36 As these groups form molecularly corrugated surfaces (Figure 2) and contain proton-active sites, they are planes of relatively high charging capacities. The (010) face is, in contrast, not only topographically flat but ideally terminated by neutrally charged and proton inactive μ-OH groups, just as in the basal plane of hematite.37,38 These important differences imply that considerably distinct water structures, hydrogen bonding patterns, electrolyte complexes, and therefore EDL structures are adopted on different planes of a single particle. They also imply that reaction free energies on the (001) face should not be impacted by those of the (010) face, and vice versa. Molecular dynamics (MD) simulations are used in this work first to resolve plausible interfacial structures adopted by water and electrolyte ions. These simulations are carried out on the (001) and (010) faces of lepidocrocite contacted with pure water, as well as aqueous solutions of sodium chloride and sodium perchlorate, and provide a means to address the impact of ions of different charge-to-size ratios lodged in highly contrasting networks of structured water molecules.17,18,39,40 The results are then used to develop a thermodynamic adsorption model that accounts for coexisting ion-specific EDL structure and capacitances on each face. Thus, by isolating electrostatic contributions from adjacent planes with distinct charging properties, the model can address distinct interfacial

in compact layer thickness and, as will be stressed in this work, capacitance caused by changes in counterion surface loadings. This study addresses this issue by developing a thermodynamic adsorption model that treats coexisting ion-specific EDL structures. The model framework proposed in this work specifically attempts to fulfill current needs for predicting the impact of surface loading-dependent variations in EDL properties. Similar needs have, for instance, been identified in the nanofluids literature28 where the importance of ion interactions, in addition to surface curvature and porosity, are identified as key factors contributing to variable compact plane capacitances. Such needs, even in tandem with earlier experiments on dropping mercury electrodes29 pointing to the importance of models predicting variable capacitance values, motivate a reinvestigation of thermodynamic adsorption modeling frameworks for mineral/water interfaces, especially now that its complexity is better appreciated. In this work a Variable Capacitance Model (VCM) is developed to account for the impact of variations in compact plane composition on capacitance, and is based on a concept originally proposed by Smit30 (Figure 1) in which a single surface can be represented by multiple coexisting EDL structures. Indirectly encompassed in this approach lies the concept that solvent reorientation caused by changes in local ionic composition and/or electric field strength, as for example conveyed in the Bockris, Devanathan, and Müller model,31 affect compact plane capacitance. In an effort to demonstrate the feasibility of this approach, the model is developed to predict p.d.i. and electrolyte ion adsorption on synthetic lepidocrocite (γ-FeOOH) particles that are commonly used in laboratory studies,32−34 and with surface structures that are analogous to those of several other naturally and industrially important iron (oxyhydr)oxide minerals.35 The focus on 2010

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SETTLE algorithm49 was used to treat water geometry and the LINCS algorithm50 to treat O−H bonds of all hydroxyls. Position restraints were not used in any other case than during simulated annealing. A 0.8 nm cutoff was used for van der Waals interactions and the particle mesh Ewald methods51 for long-range electrostatics. All calculations were carried out with Gromacs (v 4.5.3).47 Simulation cells were first energyminimized (double precision) using a steepest descent algorithm, typically in less than 104 steps, and equilibrated (single precision) by classical MD for 2 × 107 steps (10 ns). A production run of 5 ns was thereafter used to determine structural and energetic attributes of these simulation cells. 2.2. p.d.i. Adsorption at Synthetic Lepidocrocite Nanoparticle Surfaces. High precision potentiometric titrations of aqueous suspensions of lepidocrocite nanoparticles in 3, 10, and 100 mM NaCl and NaClO4 at 298 K under an atmosphere of N2(g) were carried out to determine p.d.i. loadings. Lepidocrocite particles of rod-like morphology (140− 230 nm long, 5−15 nm wide, N2(g)-B.E.T.-derived specific surface area of 77 m2/g) were synthesized, characterized, and titrated according to the methods described in Kozin et al.52 All ionic concentrations were tracked for each experimental solution, and taken specifically into account in the thermodynamic adsorption model for accurate activity coefficients and EDL property calculations. 2.3. Thermodynamic Adsorption Modeling. Speciation reactions of the (001) and (010) faces contacted with aqueous solutions of electrolyte ions were modeled using equilibrium thermodynamics. Proton and electrolyte ion adsorption reactions with surface (hydr)oxo groups of every hkl crystallographic face of lepidocrocite can be expressed with the following generic mass action equation:

phenomena taking place on different planes of multifaceted particles. A computer code for the VCM is provided in the Supporting Information (SI) section, and can be readily modified to any other mineral/water interfacial systems, and even electrolyte mixtures, of interest to the community.

2. METHODS 2.1. MD Simulations. MD simulations of the (010) and (001) faces of the γ-FeOOH phase were carried out on supercells generated with the program METADISE,41 using the crystallographic parameters of Wyckoff.42 Terminations with the smallest energy and dipole moment were chosen from the results of METADISE calculations. Dangling bonds were saturated with surface oxygens (Os) or protons, where applicable. Charge-neutral slabs were ∼3 nm thick with the following composition: Fe1188O1188(OH)990(OsH)198 for the (010) and Fe960O840(OH)840(OsH)240 for the (001) planes. The cells were repeated infinitely in all three dimensions by applying periodic boundary conditions, leaving a ∼5-nm-thick void between each slab. A MD simulation of 108 steps (10 ns) was then carried out, using a NPT (constant number of particles, constant pressure, and constant temperature) ensemble with the approach described below these lines to equilibrate bulk and surface structures. These simulations were carried out by classical MD with the CLAYFF43 force field for lattice oxygen and hydroxyls, the revised CLAYFF parameters44 for lattice Fe3+, and the flexible SPC45 force field for water. O− H bond strengths of hydroxyls of the (010) and (001) faces were constrained to the corresponding experimentally determined values in Song and Boily,34 while that of the bulk O−H bond was set to the median experimental value of lepidocrocite (3060 cm−1). Force field parameters for Na+ and Cl− were taken from Cygan et al.43 and those for ClO4− from Li and Balbuena.46 Simulations with pure water and electrolytebearing solutions confirmed that these parameters reproduce salient system properties, as detailed further in the SI. All parameter values and equations are also reported in the SI. Water was added to the ∼5-nm-thick void of the equilibrated cell using the genbox program of Gromacs (v 4.5.3),47 which sequentially solvates the system by taking into account the van der Waals radii of atoms already present. The cells were then equilibrated by MD, first by simulated annealing in one cycle from 300 to 700 K, then down to 300 K for 107 steps (1 ns), while freezing the coordinates of the bulk and surface lepidocrocite species. The cell was then simulated for another 108 steps (10 ns), by removing all position constraints and during which time the cell size relaxed and the central portion of the water layer converged to a specific density close to 1 g· cm−3. Two separate solutions of ∼1.72 mol·kg−1 sodium chloride and sodium perchlorate were thereafter created from this equilibrated cell using the genion program of Gromacs (v 4.5.3). These systems were then simulated by MD as in the case of pure water, namely, first with a period of simulated annealing followed by another 108 steps (10 ns) for further equilibration. Solutions of ∼1.72 mol·kg−1 sodium chloride and sodium perchlorate consisting of 1807 water molecules were also generated for separate sets of simulations to test modeling parameters for electrolyte ion solvation. All simulations were carried out as follows. A NPT ensemble and 0.5 fs time step were used to integrate the motion equations with the Verlet algorithm.48 The temperature of the whole system (300 K for production runs) was coupled to the velocity-rescale thermostat at a 0.1 ps relaxation time. The

a‐OH 0.5 − + bμ‐OH + cμ3 ‐O0.5 − + pn H+ + q A− + r Na + ⇌ [(‐OH1+p1)a (μ‐OH1+p2)b (μ3 ‐OH p3)c ]−0.5a − 0.5c + p1a + p2 b + p3 c ···A−q Na +r

(1)

where pn, q, and r are stoichiometric coefficients, n in pn denotes the protonation site, and A− is an anion (Cl− or ClO4−). The equilibrium constant for the reaction at a constant ionic strength is expressed as [(‐OH1+p )a (μ‐OH1+p )b (μ3 ‐OH p )c ]−0.5a − 0.5c + p1a + p2 b + p3 c ···A−q Na +r 1

2

3

[‐OH][μ‐OH][μ3 ‐O][H+]p1 + p2 + p3 [A−]q [Na +]r = Ka , b , c , p , q , r(hkl) n

(2)

In this equation the concentrations of hydroxo sites in the reactants are to the power 1, as originally suggested by Davis and Leckie,53 thus implying that ion binding to a multidentate adsorption site counts as a 1:1 interaction regardless of the siteto-ion reaction ratio. A recent article54 on the thermodynamic implications of this formulation showed that it is viable well below saturation, such as is the case for the systems under study. Electrostatic contributions to the Gibbs free energy of adsorption in this model can be readily written to be planespecific. This modeling strategy thus implies that charges of an ion adsorbing on one crystallographic face will not affect adsorption energies on another face of the same particle, and vice versa, such that 2011

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Figure 3. Representative interfacial molecular structures for the (010) (top) and (001) (bottom) planes in relation to atomic density (ρ, shown as unitless values) profiles of Figures 4 and 5.

Figure 4. Atomic density profiles perpendicular to the (001) (left) and (010) (right) faces of lepidocrocite in contact with liquid water, or aqueous solutions of 1.72 M NaCl or NaClO4. Calculated from 5 ns production runs (300 K, NVT, 107 steps). The abscissa is defined as the time-averaged distance from −OH groups of the (001) plane (left) and of μ-OH groups of the (010) plane (right). i

ΔGads(hkl) = ΔGint (hkl) +

∑ ΔziF Ψi(hkl) 0

by taking the sum of the crystal-plane specific surface charges weighted by the fraction of the area represented by plane hkl ( fs (hkl), where 1 = fs (001) + fs (010)). Charge neutrality across the o- and β-compact planes as well as the diffuse layer (dl) of the Stern Model on face hkl is then expressed as

(3)

Here, ΔGint(hkl) = −RT ln Ka,b,c,pn,q,r(hkl), F is Faraday’s constant, Δzi is the change in charge, and Ψi the surface potential at the adsorption plane i (e.g., the o-plane of the Stern model). This approach, just as the one used in an earlier study from our group,55 consequently represents an important departure from traditional thermodynamic adsorption models where surface charge is typically homogeneously distributed over the entire surface area of a particle. In this framework, the sums of the charges for all j surface species are normalized with respect to the surface area (shkl) of the face on which they occur. For instance, charges (C·m−2) of protons adsorbed in the o-plane are determined as follows:

σo , hkl + σβ , hkl + σdl, hkl = 0

The surface charge on this plane is then related to the effective overall effective capacitance (Ceff,hkl) through σo , hkl = Ceff, hkl (Ψo , hkl − Ψβ , hkl)

[(‐OH1+p1)a (μ‐OH1+p2)b (μ3 ‐OH p3)c ]−0.5a − 0.5c + p1a + p2 b + p3 c ··· ⎞ A−q Na +r ⎟⎟ ⎠

(4)

The whole-particle surface charge is therefore calculated from σo,tot =

∑hkl fs, hkl ·σo,hkl

(7)

and where Ψβ, hkl = Ψdl, hkl. Values of Ceff,hkl are determined from ion-specific values, as will be detailed in Sections 3.2 and 3.3. All compact planes are, as in traditional models but unlike Smit,30 capped by a single diffuse layer on each crystallographic hkl face, and predicted using Gouy−Chapman theory. Equilibrium concentrations of all solution and surface species can be obtained (as in standard speciation modeling codes) by solving a set of nonlinear equations representing mass action, mass balance, and charge balance equations pertaining to electrostatic attributes of the mineral/water interface. The system of equations was solved numerically using a trust region reflective algorithm and gradient estimation obtained by finitedifferencing in the computational environment of MATLAB (The Mathworks Inc.).

⎛ j F ⎜ ∑ (−0.5a − 0.5c + p1 a + p2 b + p3 c) shkl ⎜⎝ 0

σ0, hkl =

(6)

(5) 2012

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3. RESULTS AND DISCUSSION 3.1. Simulated Structures of the Lepidocrocite/Water Interface. All MD simulations reproduced bulk water, electrolyte solutions, as well as lepidocrocite bulk structures, as detailed further in the SI. Both (010) and (001) faces remained stable and neutrally charged, with surface (hydr)oxo groups persistently bound to their respective underlying structural Fe atoms throughout the course of the simulations. All surface structures contacted with pure water and aqueous solutions of sodium chloride and sodium perchlorate equilibrated well within the first 1−3 ns equilibration simulation periods. The properties of the interfacial structures and species discussed in the following sections shall nonetheless pertain to 5 ns production runs collected after the initial 10 ns equilibration period. 3.1.1. Interfacial Waters. MD simulations of the (001) and (010) faces gave rise to structured water layers as well as diverse electrolyte ion species, the dominant forms of which are shown in Figure 3. Atomic density profiles of both surfaces, shown in Figure 4, reveal four stacked water oxygen (Ow) layers starting at ∼0.6 nm from −OH on the (001) face, and ∼0.8 nm from μOH of the (010) face. The more significant layers arise at 0 and 0.22 nm on the (001) and at 0.20 and 0.40 nm on the (010) face. Although no experimental studies are yet available in the literature for lepidocrocite, these results and distances are generally comprehensible with other iron (oxyhydr)oxide/ water systems where multiple layers of water formed in highly systematic ways at surfaces with different crystallographic structures.15,56 First layer (0 nm) waters of the (001) face are lodged within interstices between −OH groups running along the c axis. As in the gas phase,36 −OH groups form intricate hydrogen bonds (H-bonds) with water. In the absence of electrolyte ions an average 0.35 bonds per group are donated to water, while 1.34 H-bonds are accepted (Table S3 of the SI). −OH groups form, in turn, a chain of hydrogen bonds (H-bonds), involving 0.36 H-bonds per group. The μ-OH and μ3-OH groups predominantly donate H-bonds to water and, together with −OH groups, control the overall orientation of first-layer water molecules, which point toward the aqueous bulk and form at a median angle of about 45° from the surface normal (Figure S1 of the SI). Second-layer (0.40 nm) waters are oriented in the opposite direction, at a median angle of about 120°, while the remaining solution-side water molecules adopt random orientations. Water populations of the (010) plane are considerably different from those of the (001) plane due to stark differences in (hydr)oxo populations and distributions. These groups donate on average 0.80 H-bonds per site and accept 0.73 Hbonds per site from first-layer (0.2 nm) water molecules (Table S3). First-layer water molecules are thus strongly oriented toward the surface, at a median angle of about 135° with the surface normal. Second-layer waters (0.40 nm) are, in contrast, more randomly oriented yet generally oriented in the opposite direction. Introducing electrolyte ions to the simulation cells has minor effects on the overall water density profiles (Figure 4) and orientations (Figure S1) on the (010) face. Similar effects were found for the analogous basal plane of hematite, even at elevated NaCl concentrations.57 The changes are, on the other hand, more substantial on the (001) plane, with a 0.05 nm shift of the second and a 0.2 nm shift of the third water layers toward

the aqueous solution. These changes are, furthermore, reflected in the hydrogen bonding populations of surface (hydr)oxo groups (Table S3). More significant changes occur in the number of −OH groups accepting H-bonds via H2O interactions, with populations decreasing from 1.34 H-bond/ site in pure water to 1.02 H-bond/site in NaCl, and 0.74 Hbond/site in NaClO4 solutions. As further described in the following section, these differences arise from important changes in the hydrogen bonding environment of surface (hydr)oxo groups in the vicinities of adsorbed electrolyte ions. These ion-specific configurations have a specific chargeneutralizing capabilities, and are thus key structures in the formulation of local EDL structures, as will be conveyed in the following sections. 3.1.2. Interfacial Ionic Species. Both (001) and (010) faces stabilize ion species of different structures and hydration state (Figures 3−5; Table S2). The (001) face accumulates 1.2 Na+

Figure 5. Ionic density profiles perpendicular to the (001) and (010) planes of lepidocrocite in contact with aqueous solutions of 1.72 M NaCl and NaClO4. Calculated from 5 ns production runs (300 K, NVT, 107 steps). Distance from the surface is defined as the timeaveraged positions of −OH groups of the (001) plane (left) and of μOH groups of the (010) plane (right).

and Cl− ions per nm2 in the NaCl medium, but 0.9 Na+ and ClO4− ions per nm2 in the NaClO4 medium.2,4 The (010) face stabilizes, in turn, 0.8 Na+ and Cl− ions per nm2 in NaCl, and 0.7 Na+ and ClO4− ions per nm2 in NaClO4. Surface complexes of chloride at the (010) face are predominantly hydrated (hydration number of nwater = ∼5− 6), while those of the (001) face occur in a ∼75:25 ratio of fully and partially hydrated ions (nwater of ∼6 and ∼4, respectively). Complexes of the (010) face occur between the first- and second-water layers, both acting as first solvation shell waters. The fully hydrated complexes of the (001) face lie within the second water layer and are also solvated by two water molecules of the first layer. Their partially dehydrated counterparts, in turn, accept hydrogen bonds from μ3-OH and μ-OH groups. Perchlorate accepts hydrogen bonds from μ-OH groups of the (010) face, as both mono- and tridentate type complexes at a ∼67:33 ratio, respectively (Figure 3), the charges of which are distributed over the same thickness of the interface. The central 2013

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Cl(VII) remains located on the solution-side of the first water layer, but the overall charge of the molecule is spread over a greater area than by chloride. In contrast, the (001) face stabilizes two distinct perchlorate species. The bidentate species, representing ∼30% of perchlorates of the compact plane, accepts hydrogen bonds from μ3-OH and μ-OH groups, with the central chloride ion between the first and second water layers. The more dominant monodentate species form, in turn, a H-bond with −OH groups and with Cl(VII) stabilized between the second and third water layers. Sodium is adsorbed as a monodentate and bidentate species on the (010) face but only bidentate species on the (001) plane. The monodentate species of the (010) face accounts for 55% of the sodium species within 0.4 nm of the surface and is fully hydrated (nwater = ∼6). The remaining 45% is directly bidentately coordinated with μ-OH groups and thus partially hydrated (nwater = ∼4). Hence, this species is 0.2 nm closer to the surface than its monodentate physisorbed counterpart, i.e., inside the first water layer. Incidentally, perchlorate increases densities of monodentate sodium species, thereby thickening the interfacial region. In contrast, sodium adsorption on the (001) face is affected neither by chloride nor by perchlorate. This predominantly yields partially hydrated (nwater = ∼4) species on two adjacent −OH species between the first and second water layers. Two of its hydration waters are first-layer waters lodged at interstices bound by rows of −OH groups. Sodium ions in a partially dehydrated state are also stabilized within those interstices, as shown by the minor density peak at 0.05 nm from the top OH groups of the (001) face. The species identified in this section consequently add support to the notion that interfacial water structures and ion identity generate ion-specific structures at the (001) and (010) faces. These different species are thereby expected to have different p.d.i. charge-neutralizing capabilities, which should in turn be accounted for by thermodynamic adsorption models. 3.2. EDL Structures. Atomic density profiles (Figures 3−5) are used to constrain possibilities for the EDL structure of the lepidocrocite/water interface. The profiles reveal clearly alternating layers of cationic and anionic species, a phenomenon highlighted in several previous experimental12,58 and theoretical16,17 studies. Positively charged layers arise from both Na+ and the central Cl(VI) atom of the perchlorate ion. These are separated by water layers, which act as solvation shells for Na+. Furthermore, Cl(VII) is generally located along the same adsorption planes as sodium. In contrast, anion-rich layers, containing Cl− and perchlorate oxo groups, tend to be concentrated within the dominant water layers, in stark contrast with classical EDL models predicting entirely chargefree water layers. These differences can be reconciled by recognizing that Cl− ions are localized at different adsorption planes from Na+ and ClO4−, and contained within their own hydration shells and local water structure. The interface could thereby be optimally described in terms of a two-dimensionally patched distribution of distinct EDL structures with their own ion-specific thicknesses and electrochemical attributes, akin to Smit’s30 original model (Figure 1). Variations in surface loadings of these ions should, moreover, produce corresponding variations in the average compact plane thickness. Representations of these ion-specific EDL structures are shown in Figure 3. Although the MD efforts of the preceding section resolved two sodium species on the (010) faces and two perchlorate species on both faces, the current discussion will consider each ion’s overall attributes to simplify the model.

These representations suggests that the (010) face should consist of substantially thicker compact planes than the (001) face, and that compact plane thickness is species-dependent. Increased perchlorate loadings, for example, would increase compact plane thickness (δ). Moreover, as long as the interfacial dielectric constant of water is not dramatically altered, the capacitances of each ion-specific region can largely related to one another by the ratio of their compact plane thicknesses, such that Cj = δref ·δj−1·Cref

(9)

where the subscript j denotes the ion for which C is to be determined from that of a reference (ref) ion. In this fashion, the capacitance of a perchlorate region at the (001) face with compact layer thickness of δ = 3.3 Å could be 2.6/3.3 = 79% of the value of a δ = 2.6 Å thick region containing chloride. Similarly, the capacitance of a sodium-bearing region (δ = 1.3 Å) could be double that of a chloride-bearing region (δ = 2.6 Å). An earlier study by Smit30 addressed such issues by expressing macroscopic interfacial properties (e.g., p.d.i. loadings, zeta potentials) in terms of a linear combination of properties of separated EDL structures. The following expression, developed along analogous lines to those of Smit,30 gives the overall effective capacitance (Ceff,hkl) of an adsorption plane by summing Cj,hkl scaled by their fractional surface loadings ( f j,hkl) Ceff, khl =

∑j

fj, khl ·C j, hkl

(10)

and where the summation is taken over the number of region within a crystallographic hkl face. This equation predicts Ceff,hkl by summing contributions from each absorbing species across all regions within a face, hence ∑j f j = 1 for j electrolyte species in a single adsorption plane. Smit,30 in contrast, included an ion-free region with its own capacitance. However, because p.d.i. cannot adsorb without background electrolytes, the structures of salt-free systems should not be entirely informative of the charge-screening capability of an interface. Values of Ceff,hkl in eq 10 are consequently generated to reflect an ion’s charge-neutralizing capability in the framework of the given interfacial ion structure and the vicinal water structure into which it is embedded. It should then follow that Ceff,hkl is an ion-loading dependent parameter, and therefore a strong function of pH, ionic strength, as well as temperature. It thereby contrasts with earlier efforts along such lines where distinct Stern layer capacitances were used to describe data below and above the pzc without any inference made to the ion loadings. The model also departs from the original Smit model30 by using only one diffuse layer across all coexisting EDL regions. 3.3. A Thermodynamic Adsorption Model. The capacitance modeling strategy presented in the preceding section can be readily implemented into a thermodynamic adsorption model, in which the Gibbs free energy of adsorption is described as the sum of intrinsic chemical and electrostatic contributions (eq 3). This model accounts for proton and electrolyte ion adsorption reactions at all structurally predicted surface sites (−OH, μ-OH, μ3-OH) on each crystallographic face of lepidocrocite. It must also assume that species identified by MD are retained and/or representative under the more dilute experimental conditions used for this work (3, 10, and 100 mM). 2014

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from the recent cryogenic XPS study of Kozin et al.52 (Figure 6). The p.d.i. adsorption data readily show that Cl− induces greater p.d.i. loading than ClO4−, a consequence of the greater charge-neutralizing capacity of this greater charge-to-size ion. The cryogenic XPS-derived ion loadings confirm, in turn, that finite levels of Na+, Cl−, and ClO4− could be on the order of 0.1−0.2 ion/nm2 (cf. Figure 6 for details of calculations from XPS data to) at the pzc, a finding falling in line with finite loadings predicted by MD. The model was developed to predict pH-independent species on the (010) face to account for the finite levels of ions at the pzc and due to the incapacity of μ-OH groups of this plane to accept protons under environmentally relevant pH conditions (Table 1). pH-dependent species on the (001) plane are, on the other hand, used to account for p.d.i. adsorption data arising from the proton active −OH and μ3-OH species. The model also simplified the speciation scheme by accounting for only one type of sodium and anionic species on each plane. Optimization of the Na- and Cl-binding constants were carried out by co-optimizing CCl only, such that CNa = δCl·δNa−1· CCl (Figure 6). This constraint thus reduces the number of adjustable parameters using a MD-derived property assuming that differences in compact plane thickness are the sole factors influencing capacitance. The best-fitting model using this methodology predicts the pH and ionic strength dependent p.d.i. loadings in NaCl media, as well as general features of the XPS-derived chloride and sodium loadings. The optimal value for the capacitance of the chloride-bearing region of CCl,001 = 2.4 Farad/m2, taken in concert with the δCl,001 = 2.6 Å value, could suggest a dielectric constant of ε = 70 for interfacial waters. If the charge were to, on the other hand, be spread over the entire particle area these values would be effectively halved to CCl,001 = 1.2 Farad/m2 and ε = 35, which tend to be more in line with current visions of mineral/water interfacial properties. These latter values would thus imply considerable amounts of defects and/or steps at the (010) face, as for instance considered by Hiemstra and van Riemsdijk.33 In fact, an ongoing study comparing the charge uptake capabilities of different types of lepidocrocite particles from our group is pointing to proton active defect site density of 0.9 site/nm2. While the current modeling strategy places these defect sites on the (010) face, the considerably more abundant 8.5 proton inactive μ-OH per nm2 is nonetheless expected to dominate the overall EDL structure. It should also be noted that a portion of these additional sites may also be located at intersections of the (010) and the edge (100) faces. Rustad and Felmy59 have in fact predicted preferential protonation at such intersections due to facilitated solvation reactions, a possibility that may justify further work in the context of the VCM. Inclusion of this charging mechanism to the model effectively predict both p.d.i. and electrolyte ion loadings (Figure 6) using a CCl,001 = 1.2 Farad/m2 value. At the same time, the model predicts strong variations in compact plane capacitance caused by variations in ionic loading and predicts strongly contrasting electrostatic potentials at both (001) and (010) faces (Figure 7), as can be expected from the different protonation constants of the outcropping (hydr)oxo groups.33 The Variable Capacitance Model developed in this work thereby represents an efficient means to predict charge development at distinct crystallographic faces of minerals, and to account for distinct p.d.i. charge-neutralizing capabilities of electrolyte ions.

Table 1. Model Parameters (100)/(001)/(010)

(010)

species

pK1,0,0,11,0,0 pK0,1,1,12,0,0 pK0,0,1,13,0,0 pK1,0,0,11,1,0 pK1,0,0,11,1,0 pK2,0,0,0,0,1 CClb CClO4b

8.5 −3.4 2pHpzc−pK1,0,0,11,0,0 −0.7 −0.8 −0.4 1.2 δCl·δ−1 ClO4·CCl,001 = 0.7

8.5a −3.4 − 0.4 0.2 −0.2 1.0 δCl·δ−1 ClO4·CCl,001 = 0.7

−OH20.5+ μ-OH20.5+ μ3-OH0.5+ −OH20.5+···Cl− −OH20.5+···ClO‑4 (−OH)2···Na+

CNab δClc δClO4c δNac ρ(−OH)d ρ(μ-OH)d ρ(μ3-OH)d

δCl·δ−1 Na·CCl,001 = 2.4 2.6 4.3 1.3 5.2 5.2 5.2

δCl·δ−1 Na·CNa,010 = 0.8 3.1 4.3 3.7 0.9a 8.5 0.0

a c

Value pertains to defect sites of the (010) face. Compact layer thickness (Å). dSites·nm−2.

b

Farad·m−2.

The set of proposed constants predicting proton and ion adsorption is shown in Table 1, and a representative MATLAB code solving for this set of equations is presented in Table S4. The model is developed to predict the experimental p.d.i. adsorption data of Figure 6 collected for this study, as well electrolyte adsorption in 10 mM NaCl and NaClO4 obtained

Figure 6. Results of thermodynamic adsorption model calculations using equations and parameters of Table 1 and generated with a code similar to that of Table S4: Ion loadings obtained by cryogenic XPS52 (a), and p.d.i. adsorption (blue = 3 mM, green = 10 mM, red = 100 mM) in NaCl (b) and NaClO4 (c). Conversion of XPS data (ion/Fe) to ion/nm2 was made using the total OH density of 12.18 site/nm2 and the overall OH/Fe ratio of 1.97, reported in Kozin et al.,52 and the assumption that XPS probes the first 2 Fe layers of the lepidocrocite surface. 2015

dx.doi.org/10.1021/la403938w | Langmuir 2014, 30, 2009−2018

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AUTHOR INFORMATION

Corresponding Author

*E-mail. [email protected]. Tel. +46 90 786 5270. Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Swedish Research Council (grant no. 2012-2976). All molecular dynamics calculations were carried out on the High Performance Computational Center North, HPC2N) cluster of the Swedish National Infrastructure for Computing at Umeå University. Philipp Kozin is thanked for collecting the potentiometric titration data. Germàn Salazar-Alvarez is thanked for collecting the transmission electron microscope images. Johannes Lützenkirchen is also thanked for initiating the thought process behind this work through discussions and preliminary modeling attempts in the late 1990s.

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Figure 7. Results of thermodynamic adsorption model calculations using equations and parameters of Table 1 and generated with a code similar to that of Table S4. Capacitance (a) and potentials developed at the (010) and (100) planes (b).

4. CONCLUSIONS This work helped forge the foundation of the VCM, a thermodynamic adsorption model accounting for the coexistence of local EDL structures with their distinct ion-specific attributes. The feasibility of this approach was demonstrated for the case of lepidocrocite surfaces contacted with aqueous solutions of NaCl and NaClO4, using MD-derived information. This model, which also isolates electrostatic contributions for separate crystallographic faces, thereby represents a significant departure from commonly used surface complexation modeling frameworks where no such phenomena are specifically taken into account. This modeling framework has excellent predictive capabilities, and is constrained by molecular-level information. The model can be readily extended to compounds of various charge-to-size ratios, as well as mixtures of background electrolytes, as for instance shown in a recent study by our group for the case of NaCl/NaClO4 solutions.60 It should, moreover, be readily applicable to a broader range of mineral/ interfacial systems where coexisting EDL structures are expected to form, or even extended to account for favored protonation reactions at intersections of crystallographic planes.

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REFERENCES

(1) Lützenkirchen, J. Surface Complexation Modelling; Academic Press, 2006; p 638. (2) Sverjensky, D. A. Prediction of Surface Charge on Oxides in Salt Solutions: Revisions for 1: 1 (M+L-) electrolytes. Geochim. Cosmochim. Acta 2005, 69 (2), 225−257. (3) Machesky, M.; Wesolowski, D.; Rosenqvist, J.; Predota, M.; Vlcek, L.; Ridley, M.; Kohli, V.; Zhang, Z.; Fenter, P.; Cummings, P. T.; Lvov, S.; Fedkin, M.; Rodriguez-Santiago, V.; Kubicki, J.; Bandura, A. Comparison of Cation Adsorption by Isostructural Rutile and Cassiterite. Langmuir 2011, 27 (8), 4585−4593. (4) Rahnemaie, R.; Hiemstra, T.; van Riemsdijk, W. H. A New Surface Structural Approach to Ion Adsorption: Tracing the Location of Electrolyte Ions. J. Colloid Interface Sci. 2006, 293 (2), 312−321. (5) Charmas, R. Four-Layer Complexation Model for Ion Adsorption at Energetically Heterogeneous Metal Oxide/Electrolyte Interfaces. Langmuir 1999, 15 (17), 5635−5648. (6) Boily, J. F.; Lutzenkirchen, J.; Balmes, O.; Beattie, J.; Sjoberg, S. Modeling Proton Binding at the Goethite (alpha-FeOOH)-Water Interface. Colloids Surf., A: Physicochem. Eng. Aspects 2001, 179 (1), 11−27. (7) Hiemstra, T.; Van Riemsdijk, W. H. On the Relationship between Charge Distribution, Surface Hydration, And the Structure of the Interface of Metal Hydroxides. J. Colloid Interface Sci. 2006, 301 (1), 1−18. (8) Hayes, K. F.; Redden, G.; Ela, W.; Leckie, J. O. Surface Complexation Models- An Evaluation of Model Parameter Estimation using FITEQL and Oxide Mineral Titration Data. J. Colloid Interface Sci. 1991, 142 (2), 448−469. (9) Stumm, W.; Hohl, H.; Dalang, F. Interaction of Metal-Ions with Hydrous Oxide Surfaces. Croatica Chemica Acta 1976, 48 (4), 491− 504. (10) Davis, J. A.; Kent, D. B. Surface Complexation Modeling in Aqueous Geochemistry. Rev. Mineral. 1990, 23, 177−260. (11) Schindler, P. W.; Gamsjäger, H. Acid-Base Reactions of TiO2 (Anatase) - Water Interface and Point of Zero Charge of TiO2 Suspensions. Kolloid Z. Z. Polym. 1972, 250 (7), 759. (12) 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 (23), 8637−8650. (13) Ghose, S. K.; Waychunas, G. A.; Trainor, T. P.; Eng, P. J. Hydrated Goethite (α-FeOOH) (100) Interface Structure: Ordered Water and Surface Functional Groups. Geochim. Cosmochim. Acta 2010, 74 (7), 1943−1953.

ASSOCIATED CONTENT

S Supporting Information *

Detailed methods and discussions of molecular dynamics simulation results (hydrogen bonding, surface oxo-electrolyte ion distances, water orientation, atomic density, and net charge profiles). MATLAB code for a solving a simplified system of equations under the VCM. This material is available free of charge via the Internet at http://pubs.acs.org. 2016

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(14) Sakuma, H.; Kawamura, K. Structure and Dynamics of Water on Li+-, Na+-, K+-, Cs+-, H3O+-Exchanged Muscovite Surfaces: A Molecular Dynamics Study. Geochim. Cosmochim. Acta 2011, 75 (1), 63−81. (15) Fenter, P.; Sturchio, N. C. Mineral-Water Interfacial Structures Revealed by Synchrotron X-ray Scattering. Prog. Surf. Sci. 2004, 77 (5− 8), 171−258. (16) Kerisit, S.; Cooke, D. J.; Marmier, A.; Parker, S. C. Atomistic Simulation of Charged Iron Oxyhydroxide Surfaces in Contact with Aqueous Solution. Chem. Commun. 2005, 24, 3027−3029. (17) Kerisit, S.; Ilton, E. S.; Parker, S. C. Molecular Dynamics Simulations of Electrolyte Solutions at the (100) Goethite Surface. J. Phys. Chem. B 2006, 110 (41), 20491−20501. (18) Bourg, I. C.; Sposito, G. Molecular Dynamics Simulations of the Electrical Double Layer on Smectite Surfaces Contacting Concentrated Mixed Electrolyte (NaCl-CaCl2) Solutions. J. Colloid Interface Sci. 2011, 360 (2), 701−715. (19) Rietra, R.; Hiemstra, T.; van Riemsdijk, W. H. Electrolyte Anion Affinity and Its Effect on Oxyanion Adsorption on Goethite. J. Colloid Interface Sci. 2000, 229 (1), 199−206. (20) Bousse, L. D.; NF; Bergveld, P. Operation of Chemically Sensityive Field-Effect Sensors As a Function of the InsulatorElectrolyte Interface. IEEE Trans. Electron Devices 1983, 30 (10), 1263−1270. (21) Barrow, N.; B., J. W.; Posner, A. M.; Quirk, J. P. Describing the Adsorption of Copper, Zinc and Lead on a Variable Charge Mineral Surface. Aust. J. Soil Res. 1981, 19 (4), 309−321. (22) Hiemstra, T.; VanRiemsdijk, W. H. A Surface Structural Approach to Ion Adsorption: The Charge Distribution (CD) Model. J. Colloid Interface Sci. 1996, 179 (2), 488−508. (23) Hiemstra, T.; Rahnemaie, R.; van Riemsdijk, W. H. Surface Complexation of Carbonate on Goethite: IR Spectroscopy, Structure and Charge Distribution. J. Colloid Interface Sci. 2004, 278 (2), 282− 290. (24) Rahnemaie, R.; Hiemstra, T.; van Riemsdijk, W. H. Carbonate Adsorption on Goethite in Competition with Phosphate. J. Colloid Interface Sci. 2007, 315 (2), 415−425. (25) Hiemstra, T.; Van Riemsdijk, W. H. Fluoride Adsorption on Goethite in Relation to Different Types of Surface Sites. J. Colloid Interface Sci. 2000, 225 (1), 94−104. (26) Boily, J.-F.; Sjöberg, S.; Persson, P. Structures and Stabilities of Cd(II) and Cd(II)-Phthalate Complexes at the Goethite/Water Interface. Geochim. Cosmochim. Acta 2005, 69 (13), 3219−3235. (27) Boily, J. F. Charge Localization in Cation-Sulfate Complexes: Implications for Thermodynamic Surface Complexation Models of the Mineral/Water Interface. J. Phys. Chem. C 2007, 111 (3), 1299−1306. (28) Kant, R.; Singh, M. B. Generalization of the Gouy-ChapmanStern Model of an Electric Double Layer for a Morphologically Complex Electrode: Deterministic and Stochastic Morphologies. Phys. Rev. E 2013, 88 (5). (29) Macdonald, J. R.; Barlow, C. A. Theory of Double-Layer Differential Capacitance in Electrolytes. J. Chem. Phys. 1962, 36 (11), 3062−&. (30) Smit, W. Surface Complexation Constance of the Site Binding Model. J. Colloid Interface Sci. 1986, 113 (1), 288−291. (31) Bockris, J. O. M.; Devannathan, M. A. V.; Müller, K. Proc. R. Soc. London, Ser. A 1963, A274. (32) Manceau, A.; Nagy, K. L.; Spadini, L.; Ragnarsdottir, K. V. Influence of Anionic Layer Structure of Fe-Oxyhydroxides on the Structure of Cd Surface Complexes. J. Colloid Interface Sci. 2000, 228 (2), 306−316. (33) Hiemstra, T.; van Riemsdijk, W. H. Adsorption and Surface Oxidation of Fe(II) on Metal (Hydr)oxides. Geochim. Cosmochim. Acta 2007, 71 (24), 5913−5933. (34) Song, X. W.; Boily, J. F. Structural Controls on OH site Availability and Reactivity at Iron Oxyhydroxide Particle Surfaces. Phys. Chem. Chem. Phys. 2012, 14 (8), 2579−2586. (35) Schwertmann, U.; Cornell, R. M. The iron oxides: structure, properties, reactions, occurrences and uses; Wiley-VCH: Weinheim, 2003.

(36) Song, X. W.; Boily, J. F. Surface Hydroxyl Identity and Reactivity in Akaganeite. J. Phys. Chem. C 2011, 115 (34), 17036− 17045. (37) Shimizu, K.; Shchukarev, A.; Boily, J. F. X-ray Photoelectron Spectroscopy of Fast-Frozen Hematite Colloids in Aqueous Solutions. 3. Stabilization of Ammonium Species by Surface (Hydr)oxo Groups. J. Phys. Chem. C 2011, 115 (14), 6796−6801. (38) Venema, P.; Hiemstra, T.; Weidler, P. G.; van Riemsdijk, W. H. Intrinsic Proton Affinity of Reactive Surface Groups of Metal (Hydr)Oxides: Application to Iron (Hydr)Oxides. J. Colloid Interface Sci. 1998, 198 (2), 282−295. (39) Tournassat, C.; Chapron, Y.; Leroy, P.; Bizi, M.; Boulahya, F. Comparison of Molecular Dynamics Simulations with Triple Layer and Modified Gouy-Chapman Models in a 0.1 M NaCl-montmorillonite System. J. Colloid Interface Sci. 2009, 339 (2), 533−541. (40) Wang, J. W.; Kalinichev, A. G.; Kirkpatrick, R. J. Asymmetric Hydrogen Bonding and Orientational Ordering of Water at Hydrophobic and Hydrophilic Surfaces: A Comparison of Water/Vapor, Water/Talc, and Water/Mica Interfaces. J. Phys. Chem. C 2009, 113 (25), 11077−11085. (41) Watson, G. W.; Kelsey, E. T.; deLeeuw, N. H.; Harris, D. J.; Parker, S. C. Atomistic Simulation of Dislocations, Surfaces and Interfaces in MgO. J. Chem. Soc. Faraday Trans. 1996, 92 (3), 433− 438. (42) Wyckoff, R. W. G. Crystal Structures 1, 1963 ed.; Interscience Publishers: New York, 1963. (43) Cygan, R. T.; Liang, J. J.; Kalinichev, A. G. Molecular Models of Hydroxide, Oxyhydroxide, And Clay Phases and the Development of a General Force Field. J. Phys. Chem. B 2004, 108 (4), 1255−1266. (44) Kerisit, S. Water Structure at Hematite−Water Interfaces. Geochim. Cosmochim. Acta 2011, 75 (8), 2043−2061. (45) Teleman, O.; Jonsson, B.; Engstrom, S. A Molecular-Dynamics Simulation of a Water Model with Intermolecular Degrees of Freedom. Mol. Phys. 1987, 60 (1), 193−203. (46) Li, T.; B, P. B. J. Electrochem. Soc. 1999, 146, 3613−3622. (47) van der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. GROMACS: Fast, Flexible, And Free. J. Comput. Chem. 2005, 26 (16), 1701−1718. (48) Hockney, R. W.; Goel, S. P.; Eastwood, J. W. Quiet HighResolution Computer Models of a Plasma. J. Comput. Phys. 1974, 14 (2), 148−158. (49) Miyamoto, S.; Kollman, P. A. SETTLE - an Analyical Version of the Shake and Rattle Algorithm for Rigid Water Models. J. Comput. Chem. 1992, 13 (8), 952−962. (50) Hess, B.; Bekker, H.; Berendsen, H. J. C.; Fraaije, J. LINCS: a Linear Constraint Solver for Molecular Simulations. J. Comput. Chem. 1997, 18 (12), 1463−1472. (51) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A Smooth Particle Mesh Ewald Method. J. Chem. Phys. 1995, 103 (19), 8577−8593. (52) Kozin, P. A.; Shchukarev, A.; Boily, J.-F. Electrolyte Ion Binding at Iron Oxyhydroxide Mineral Surfaces. Langmuir 2013, 29, 12129− 12137. (53) Davis, J. A.; Leckie, J. O. Surface Ionization and Complexation at Oxide-Water Interface. 2. Surface Properties of Amorphous Iron Oxyhydroxide and Adsorption of Metal Ions. J. Colloid Interface Sci. 1978, 67 (1), 90−107. (54) Wang, Z. M.; Giammar, D. E. Mass Action Expressions for Bidentate Adsorption in Surface Complexation Modeling: Theory and Practice. Environ. Sci. Technol. 2013, 47 (9), 3982−3996. (55) Kozin, P. A.; Boily, J.-F. Proton Binding and Ion Exchange at the Akaganéite/Water Interface. J. Phys. Chem. C 2013, 117 (12), 6409− 6419. (56) Ghose, S. K.; Waychunas, G. A.; Trainor, T. P.; Eng, P. J. Hydrated Goethite (alpha-FeOOH) (100) Interface Structure: Ordered Water and Surface Functional Groups. Geochim. Cosmochim. Acta 2010, 74 (7), 1943−1953. (57) Spagnoli, D.; Cooke, D. J.; Kerisit, S.; Parker, S. C. Molecular Dynamics Simulations of the Interaction between the Surfaces of Polar 2017

dx.doi.org/10.1021/la403938w | Langmuir 2014, 30, 2009−2018

Langmuir

Article

Solids and Aqueous Solutions. J. Mater. Chem. 2006, 16 (20), 1997− 2006. (58) 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 (22), 16647−16651. (59) Rustad, J. R.; Felmy, A. R. The Influence of Edge Sites on the Development of Surface Charge on Goethite Nanoparticles: A Molecular Dynamcis Investigations. Geochim. Cosmochim. Acta 2005, 69 (6), 1405−1411. (60) Kozin, P. A.; Boily, J. F. Mineral Surface Charge Development in Mixed Electrolyte Solutions. J. Colloid Interface Sci. 2014, 418, 245− 253.

2018

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