Electrostatic Potential of Specific Mineral Faces - American Chemical

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Electrostatic Potential of Specific Mineral Faces P. Zarzycki,*,† S. Chatman,† T. Preo
canin,‡ and K. M. Rosso† † ‡

Pacific Northwest National Laboratory, Richland, Washington, United States Department of Chemistry, University of Zagreb, Croatia

bS Supporting Information ABSTRACT: Reaction rates of environmental processes occurring at hydrated mineral surfaces are in part controlled by the electrostatic potential that develops at the interface. This potential depends on the structure of exposed crystal faces as well as the pH and the type of ions and their interactions with these faces. Despite its importance, experimental methods for determining fundamental electrostatic properties of specific crystal faces such as the point of zero charge are few. Here we show that this information may be obtained from simple, cyclic potentiometric titration using a wellcharacterized single-crystal electrode exposing the face of interest. The method exploits the presence of a hysteresis loop in the titration measurements that allows the extraction of key electrostatic descriptors using the Maxwell construction. The approach is demonstrated for hematite (R-Fe2O3) (001), and thermodynamic proof is provided for the resulting estimate of its point of zero charge. Insight gained from this method will aid in predicting the fate of migrating contaminants, mineral growth/dissolution processes, and mineral
microbiological interactions and in testing surface complexation theories.

’ INTRODUCTION The mineral/aqueous-phase interface is one of the largest charged interfaces on Earth. A majority of environmentally relevant processes, such as ionic speciation, pollutant retardation, mineral transformation, and microbiological and catalytic processes, occur at this interface.1
3 One of the most distinctive features of this interface is the electrostatic potential gradient generated by the separation of charged groups at the mineral surface and compensating counterions in solution, the so-called electrical double layer. Understanding how this potential develops and its characteristics is crucial for a detailed comprehension of environmental and geochemical processes. After decades of research, the charging mechanism is rather well understood, attributed primarily to Hþ uptake/release by the mineral surface.1
5 As a result, interfacial electrostatics is primarily controlled by the solution pH. In both experimental and theoretical studies, interfacial charging properties are quantitatively described using only a few characteristic pH values at which the surface charge (point of zero charge, PZC), surface potential (point of zero potential, PZP), and ζ potential (isoelectric point, IEP) become zero.4,5 The PZC is the most frequently reported value; when pH = PZC, the net surface charge is equal to zero by definition. It also therefore defines pH ranges where a surface is net positively charged (pH < PZC) or net negatively charged (pH > PZC). Unless aqueous ions are specifically interacting with the surface (e.g., by covalent bonds with partial ion dehydration), the PZC encompasses all other parameters (PZC = PZP = IEP) and therefore it alone suffices to describe the charging properties of a mineral surface fully. To r 2011 American Chemical Society

avoid confusion regarding different definitions of the point of zero charge, which can further specify the given mineral/electrolyte interface,6 here for simplicity we assume a lack of specific ion adsorption and therefore use the term PZC in its generalized form. The PZC is sensitive to the mineral type, surface orientation, stoichiometry, morphology, sample preparation, and the presence of ions, in principle enabling the detection of subtle interfacial properties or reactions by this quantity. For example, it has been postulated that structural differences among various crystal faces of the same mineral manifest themselves in different PZC values.7,8 Unfortunately, the PZC values of specific crystal faces have so far proven very difficult to determine and are thus rarely reported, despite their fundamental importance. Rather, PZC values are typically determined for minerals in a polycrystalline powdered form, which consequently represents an average over all crystal faces exposed on particles.3
5 Experimentally determined PZC values for specific crystal faces have therefore remained a kind of Holy Grail of aquatic mineral surface chemistry for decades. One of the earliest attempts to fill this scientific gap was based on developing synthesis methods that enabled shape and size control of grown mineral crystallites, from which particles exposing a predominant set of crystal faces were produced.9 Almost concurrently, single crystals with a well-defined surface were used in combination with sum-frequency generation spectroscopy10
14 Received: April 14, 2011 Revised: May 31, 2011 Published: June 08, 2011 7986

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Langmuir and/or scanning probe microscopy.15
17 Unfortunately, those methods are not routinely used in many laboratories, and their performance for this purpose often depends on sample preparation or a chosen model for data interpretation. A promising method that could become a new laboratory standard is the single-crystal electrode (SCrE) approach introduced by Kallay and co-workers.18
20 Their technique is to combine simple and well-understood potentiometric acid
base titration with a single-crystal working electrode that isolates and exposes the crystal face of interest to the electrolyte. The SCrE method conveniently detects changes in the surface electrostatic potential with pH relative to a standard reference electrode. There are, however, a few limitations of this method that have hindered its application. One of the most striking is that it does not directly provide a PZC value nor the absolute value of the surface potential. Instead, the observable SCrE is the overall electromotive force (emf) of the cell as a function of pH. In addition, cyclic titration from acidic to basic pH (alkalimetric) and the reverse (acidimetric) often shows hysteresis,19 which so far has made the extraction of a PZC value ambiguous. Despite these apparent difficulties, this SCrE approach has initiated a remarkable revival of classical surface electrochemistry techniques, such as potentiometric titration and streaming potential measurements, applied to the study of specific hydrated mineral surfaces (e.g., refs 21
26). In this report, we show how limitations of SCrE measurements can be overcome through the careful thermodynamic analysis of cyclic titration. In particular, we exploit titration hysteresis as the key informing phenomenon for PZC determination. Our methodology is illustrated by determining the PZC for the (001) face of hematite (R-Fe2O3), a commonly occurring iron oxide mineral27,28 and a prominent case study. We also address reported differences in the electrostatic properties of hematite (001) (or isostructural corundum, R-Al2O3) that have puzzled the surface science community for years.10
16 In contrast to other stable faces, nominally all (001) surface oxygen atoms are doubly coordinated (commonly denoted as tFe2O). The PZC of this highly uniform surface therefore correlates directly to the energetics of Hþ binding to tFe2O sites (tAl2O in the case of corundum) in situ. Despite many attempts,10
20,25,26 the PZC determination for this surface has proven elusive.

LETTER

titration path is proportional to the hysteresis loop area (A), that is,  I  ba
ψ dpH ð1Þ ΔG µ A where A ¼ ψab 0 0 where ψab 0 is the surface potential measured during alkalimetric titration (ab, from acidic to basic pH), ψba 0 is the surface potential measured during acidimetric titration (ba, from basic to acidic pH), and the integration represents the summation along the cyclic titration path. The surface potential is directly related to the measured electromotive force of the cell (E) according to the relation ψ0 ¼ E
ET

where ET represents all pH-independent contributions to the measured potential, for instance, with the contact resistance arising from Schottky barriers (details in Supporting Information). In a standard SCrE measurement, the ET shift is unknown, and a value is estimated or an arbitrary value is chosen (often taken from an independent ζ-potential measurement or the potentiometric titration of a powdered mineral).18
20 As we will show later, ET can be easily determined in the hysteresis analysis of a cyclic titration experiment. In a fully equilibrated titration cycle in which reversibility is achieved at each pH step, ΔG becomes independent of the titration path. Consequently, the work done along the cyclic titration path is zero unless there is a dissipative energy leak. This requirement is satisfied under equilibrium titration conditions, which do not exhibit hysteresis. In the case of nonequilibrium titration, the requirement of zero free energy along the cyclic titration path can be exploited to gain more information about the system, implemented using the Maxwell construction (theorem of equal area). Specifically, the cyclic titration path is conceptually divided into a region where protons are predominantly adsorbed to the surface and another where they are predominantly released from the surface in response to a change in pH (Figure 1a). The concept is expressed by the following equation (where the surface potential is replaced by the measured electromotive force of the cell)   Z pHb  Z pHPZC  Eab
Eba dpH ¼ Eab
Eba dpH ð3Þ pHa

’ THEORY Titration hysteresis arises from the lag in electrode potential response to changes in the bulk solution pH along the titration path.19 On the basis of acid
base potentiometric titration principles, the bulk Hþ concentration decreases after the addition of an aliquot of base during alkalimetric titration, which induces the release of protons bound to the surface, whereas during acidimetric titration the addition of acid increases the bulk Hþ concentration, resulting in Hþ adsorption. Unfortunately, fixed time intervals between subsequent titrant additions typically prevent the surface from reaching equilibrium with solution pH adjustments. Not all Hþ ions are able to leave the surface before the next incremental bulk pH increase during alkalimetric titration, which results in a higher positive potential than expected at equilibrium. The opposite effect takes place during acidimetric titration. It can be shown that the infinitesimal change in free energy in a potentiometric titration step is proportional to
ψ0 dpH (details in Supporting Information). The work done along the cyclic

ð2Þ

pHPZC

where pHPZC is the pH at which the hysteresis loop is divided into equal areas, pHa and pHb are the most acidic and most basic pH values explored during the titration cycle, and Eab and Eba stand for the emf of the cell measured in alkalimetric and acidimetric titration directions, respectively. This approach takes advantage of the fact that the hysteresis area is directly proportional to the work done on/by the system during a titration cycle as explained above. By reformulating the hysteresis problem in this way and based on the definition of the PZC (i.e., the pH at which the net surface potential is zero in the absence of specific adsorption), one can conclude that the dividing pH corresponds to the PZC (Supporting Information). Besides its simplicity, this method has another striking advantage, namely, the PZC of an individual crystal face can be directly extracted from hysteretic titration experiments without any assumption of the titration mechanism or stoichiometry of charging/discharging surface groups. At the same time, by knowing the PZC value, the emf recorded anywhere along the titration curve can thus be converted into the actual surface potential. Because the surface 7987

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LETTER

Figure 1. Potentiometric titration hysteresis loop for (001) hematite (a) (30 min titration intervals, 0.1 mol/dm3 NaNO3). Schematic representation of the Maxwell construction shown in the inset. Titration curve and error bars were obtained by averaging a series of eight titration experiments. Atomic force microscope topographs of the electrode surface (b) before and (c) after titration. Experimental and theoretical details are provided in the Supporting Information.

potential at pH = PZC should be zero, any residual emf at this pH represents contributions to the potential unrelated to the formation of the electrical double layer at the single-crystal electrode surface. This residual therefore estimates the shift (noted as ET in Figure 1a and in eq 2) that can be applied to the whole titration curve. In practice, ET can then be estimated as the potential midpoint between alkalimetric and acidimetric titration curves at pH = PZC: 1 ET ¼ ðEab ðpHPZC Þ þ Eba ðpHPZC ÞÞ 2

ð4Þ

It is worth mentioning that the lag observed in cyclic titration can arise directly from the kinetics of surface sorption. Unfortunately, application of the Maxwell construction formalism expressed via rate equations would require many assumptions on protonation mechanisms/kinetics and measurements of the time-dependent surface concentrations. The presented thermodynamic approach is based only on the requirement of freeenergy conservation along the hysteresis loop and can be applied without any assumptions about the protonation mechanism. An extended discussion is presented in the Supporting Information.

’ RESULTS AND CONCLUSIONS Although applicable to any mineral surface whose cyclic titration yields hysteresis, here we demonstrate the method by determining the PZC for hematite (001), motivated by earlier studies on the same surface and that of isostructural corundum crystals.10
12,17,25,26 Previous studies have postulated that the PZC for corundum (001) should be about 3 to 4 pH units below that determined for the polycrystalline mineral powder. In the case of hematite, a similar shift was put forward on the basis of the valence-bond surface complexation model developed by Hiemstra and van Rijemsdijk (known as the multisite complexation model, MUSIC).7,8 More precisely, the MUSIC model predicts the PZC of structurally perfect hematite (001), exclusively covered in doubly coordinated hydroxyl groups, to be about 5.96, approximately 1
3 pH units below the PZC for polycrystalline hematite powder (e.g., pH 7
9).29
31 Unfortunately, only one measured value for the PZC of hematite (001) has been reported (i.e., pH 8
8.5),15,16 and it is in the range of polycrystalline hematite. SCrE measurements in the present study performed with the methods described above predict that the PZC of the hematite (001) surface is approximately 8 (Figure 1a). The experiments 7988

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Figure 2. Composition of hematite (001): (a) Dominant doubly coordinated surface oxygen atoms and singly coordinated groups formed as a result of surface and subsurface defects (e.g., steps). Two types of singly coordinated groups are denoted as Fe1Olong (less acidic, rFe
O = 2.12 Å) and Fe1Oshort (more reactive, rFe
O = 1.95 Å). The dominant, doubly coordinated surface groups are denoted as Fe2O. (See Venema et al.7) According to the multisite complexation model, the proton affinities for those groups (hypothetical PZC) are7 5.96, 13.65, and 18.05 for Fe2O, Fe1Oshort, and Fe1Olong, respectively.

were repeated several times with freshly prepared surfaces as well as with differently chosen titration time intervals. All performed titrations confirm the high PZC of the (001) surface, in agreement with the previously reported data by Eggleston and Jordan.15 In addition, a systematic decrease in the hysteresis area is observed as expected, with increasing equilibration time, confirming the kinetic (nonequilibrium) origin of hysteresis. In such a measurement, it is important to ensure that no significant transformations of the surface have occurred. Except for the appearance of small quantities of ferric hydroxide gel due to slight acidic dissolution at low pH, atomic force microscopy of the electrode surface before and after titration measurements shows only well-ordered hematite (001) surface features (Figure 1b,c). Our measured PZC value is much higher than the MUSIC model prediction (∼6), and it disagrees with the expected acidic shift for (001) surfaces relative to bulk powder forms. This result can be explained by the unavoidable presence of structural defects at the surface that provide a fraction of less-acidic, singly and possibly triply coordinated sites. Step edges are one such defect notably present (Figure 1b,c). However, comprehensive AFM imaging shows that their areal density is only ∼2% (Supporting Information), which does not provide enough less-acidic sites to shift the observed PZC to 8. We conclude, therefore, that the singly and/or triply coordinated sites are also present in the form of point defects at the surface beyond the resolution of AFM. Cationic vacancies near the surface region are likely as well as consistent with our model for the higher PZC; their presence was suggested previously by Hiemstra, van Riemsdijk, and co-workers,7,16 and was deduced using scanning tunneling microscopy by Eggleston.31 In addition, by applying Prelot and co-workers’32,33 approach to analyzing the derivative of potentiometric titration data (titration derivative isotherm summation method, TDIS), we confirmed the presence of doubly coordinated groups with a proton affinity constant (pK) of 6 (excellent agreement with the MUSIC model) and a shift in proton affinity caused by less-acidic sites. Details can be found in the Supporting Information.

LETTER

Figure 3. Grand canonical Monte Carlo simulation of cyclic potentiometric titration for a simple square lattice model of metal oxide (100  100 surface sites)34
36 with lateral interactions described by the Borkovec potential.32,33 Simulation parameter values are equal to those used by Borkovec.31 Kinetic lag was obtained by sampling before the complete charge balance for each pH step was achieved. Details can be found in the Supporting Information. The PZC estimated using the hysteresis method is exactly equal to the PZC obtained from completely equilibrated simulations.

In addition to the experimental study, we simulated the mechanism of hysteresis loop formation using a kinetically constrained grand canonical Monte Carlo simulation scheme, as originally proposed by Borkovec34,35 and later extended in our group.36
38 For methodological details, see the Supporting Information section. As shown in Figure 3, by imposing a time restriction on lattice model equilibration we were able to reproduce the hysteresis phenomenon for surface charging curves, whose analysis provides exactly the same PZC value as obtained from fully equilibrated simulations. The presented methodology stands ready to be applied to a wide range of mineral surfaces. It is anticipated that steadily increasing experimental access to the electrostatic properties of specific mineral/aqueous phase interfaces will ultimately help unveil answers to pressing geochemical questions about surface structure
reactivity relationships, effects of the electrostatic surface potential on rates and chemical pathways of mineral transformation and charge transfer, and the fate and transport of contaminants in subsurface environments.

’ ASSOCIATED CONTENT

bS

Supporting Information. Derivation of the thermodynamic proof of concept, possible sources of inaccuracies, details of experimental and simulation procedures, and information about relevant available GUI software developed for the automatic analysis of experimental titration hysteresis data. This material is available free of charge via the Internet at http:// pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] or [email protected]. Tel: 509371642. 7989

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’ ACKNOWLEDGMENT This work was supported by a grant from the U.S. Department of Energy (DOE), Office of Basic Energy Sciences, Geosciences Program. The research was performed using the Environmental Molecular Sciences Laboratory (EMSL), a national scientific user facility, sponsored by the DOE Office of Biological and Environmental Research located at Pacific Northwest National Laboratory. T.P. was also supported by the Ministry of Science, Education and Sports of the Republic of Croatia (project no. 119-1191342-2961). ’ REFERENCES (1) Brown, G. E.; Henrich, V. E.; Casey, W. H.; Clark, D. L.; Eggleston, C.; Felmy, A.; Goodman, D. W.; Gr€atzel, M.; Maciel, G.; McCarthy, M. I.; Nealson, K. H.; Sverjensky, D. A.; Toney, M. F.; Zachara, J. M. Chem. Rev. 1999, 99, 77–174. (2) Al-Abadleh, H. A.; Grassian, V. H. Surf. Sci. Rep. 2003, 52, 63–161. (3) Stumm, W.; Morgan, J. J. Aquatic Chemistry, 3rd ed.; Wiley: New York, 1996. (4) Dzombak, D. A.; Morel, F. M. M. Surface Complexation Modeling: Hydrous Ferric Oxide; Wiley: New York, 1990. (5) L€utzenkirchen, J., Ed. Surface Complexation Modelling; Elsevier: Amsterdam, 2006. (6) Sposito, G. Environ. Sci. Technol. 1998, 32, 2815–2819. (7) Venema, P.; Hiemstra, T.; Weidler, P. G.; van Riemsdijk, W. H. J. Colloid Interface Sci. 1998, 198, 282–295. (8) Hiemstra, T.; Venema, P.; van Riemsdijk, W. H. J. Colloid Interface Sci. 1996, 184, 680–692. (9) Sugimoto, T.; Wang, Y. J. Colloid Interface Sci. 1998, 207, 137–149. (10) Stack, G.; Higgins, S. R.; Eggleston, C. M. Geochim. Cosmochim. Acta 2001, 65, 3055–3063. (11) Fitts, J. P.; Shang, X.; Flynn, G. W.; Heinz, T. F.; Eisenthal, K. B. J. Phys. Chem. B 2005, 109, 7981–7986. (12) Fitts, J. P.; Machesky, M. L.; Wesolowski, D. J.; Shang, X.; Kubicki, J. D.; Flynn, G. W.; Heinz, T. F.; Eisenthal, K. B. Chem. Phys. Lett. 2005, 411, 399–403. (13) Zhang, L.; Tian, C.; Waychunas, G. A.; Shen, Y. R. J. Am. Chem. Soc. 2008, 130, 7686–7694. (14) Braunschweig, B.; Eissner, S.; Daum, W. J. Phys. Chem. C 2008, 113, 1751–1754. (15) Eggleston, C. M.; Jordan, G. Geochim. Cosmochim. Acta 1998, 62, 1919–1923. (16) Hiemstra, T.; van Riemsdijk, W. H. Langmuir 1999, 15, 8045–8051. (17) Franks, G. V.; Meagher, L. Colloids Surf., A 2003, 214, 99–110.
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