the signiﬁcance of surface complexation reactions in hydrologic...

Review

The significance of surface complexation reactions in hydrologicsystems: a geochemist’s perspective

C. Koretsky*

School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, GA 30332, USA

Received 26 March 1999; received in revised form 16 December 1999; accepted 10 February 2000

Abstract

Complexation reactions at the mineral–water interface affect the transport and transformation of metals and organiccontaminants, nutrient availability in soils, formation of ore deposits, acidification of watersheds and the global cycling ofelements. Such reactions can be understood by quantifying speciation reactions in homogeneous aqueous solutions, character-izing reactive sites at mineral surfaces and developing models of the interactions between aqueous species at solid surfaces. Inthis paper, the application of thermodynamic principles to quantify aqueous complexation reactions is described. This isfollowed by a brief overview of a few of the methods that have been used to characterize reactive sites on mineral surfaces.Next, the application of empirical and semi-empirical models of adsorption at the mineral–water interface, including distribu-tion coefficients, simple ion exchange models, and Langmuir and Freundlich isotherms is discussed. Emphasis is placed on thelimitations of such models in providing an adequate representation of adsorption in hydrological systems. These limitationsarise because isotherms do not account for the structure of adsorbed species, nor do they account for the development of surfacecharge with adsorption. This is contrasted with more sophisticated models of adsorption, termed ‘surface complexationmodels’, which include the constant capacitance model, the diffuse layer model, the triple layer model and the MUSICmodel. In these models, speciation reactions between surface functional groups and dissolved species control the variablesurface charge build-up and the specific adsorption properties of minerals in aqueous solutions. Next, the influence of mineralsurface speciation on the reactivity of adsorbed species and on far from equilibrium dissolution rates of minerals is discussed.Finally, the applicability of microscopic models of surface complexation to field-scale systems is explored and the need tointegrate sophisticated surface chemical and hydrological modeling approaches is stressed.q 2000 Elsevier Science B.V. Allrights reserved.

Keywords: Surface complexation; Chemical weathering; Water–rock interactions; Sorption; Mineral surface; Geochemistry

1. Introduction

As anthropogenic contaminants reach ever greaterportions of the hydrosphere, the development of quan-titative methods to predict the fate of contaminantsboth within homogeneous aqueous solutions and in

contact with mineral surfaces is becomingincreasingly important. The eventual fate of contami-nants, such as heavy metals or organic species,depends not only on transport processes but also ongeochemical reactions, especially those involvingmineral–water interfaces. The movement of metalsand other chemical species through an aquifer maybe either greatly retarded or enhanced by reactionsoccurring at mineral surfaces. For example, acidicleachates from landfills may initially be buffered by

Journal of Hydrology 230 (2000) 127–171

0022-1694/00/$ - see front matterq 2000 Elsevier Science B.V. All rights reserved.PII: S0022-1694(00)00215-8

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* Present address: Department of Geology, Western MichiganUniversity, Kalamazoo, MI 49008, USA.

E-mail address:[email protected] (C. Koretsky).

alkaline soils and groundwaters. Transport of heavymetals in the leachate will initially be retarded bysorption at soil mineral surfaces. However, once thebuffering capacity of the soil is depleted, the pH willdecrease precipitously, potentially leading to deso-rption and transport of heavy metal pulses of higherconcentration than that of the initial leachate (Hoste-tler and Erikson, 1993; Criscenti, 1996). The migra-tion of potentially hazardous organic contaminants isalso affected by reactions at the mineral surface. Forexample, the rates of some abiotic organic degrada-tion reactions, such as ester hydrolysis, are enhancedby the presence of oxide surfaces (Stone, 1989a).

Reactions at mineral–water interfaces are alsoimportant in determining the chemical speciation ofnatural, unpolluted soil solutions, which, in turn,controls the availability of both nutrients and toxinsfor uptake by plants. In sandy soils, for example, theamount of phosphate available to plants may belimited by the abundance of aluminum and ironoxide minerals which provide sites for phosphateadsorption (Borggaard et al., 1990). The redox stateof soil solutions and the associated surface speciationmay also play an important role in determining thelevels of available micronutrients, many of whichare required by plants at low concentrations but aretoxic at higher concentrations (Logan and Traina,1993).

Reactions at the mineral–water interface are furtherinvolved in many other geologic processes. It hasbeen suggested that adsorption and reduction reac-tions on sulfide mineral surfaces play a significantrole in the formation of gold ore deposits (Bancroftand Hyland, 1990) and that hydrothermal leachingmay contribute to the formation of many ore deposits(Hochella and White, 1990; Skinner, 1997). There isalso a great deal of evidence suggesting that the far-from-equilibrium dissolution rates of rock-formingminerals are controlled by reactions at the mineralsurface (Fu¨rrer and Stumm, 1986; Wieland et al.,1988; Stumm, 1992).

To quantify processes as diverse as contaminantdegradation, nutrient cycling in soils, ore depositformation, or chemical weathering, it is first necessaryto quantify chemical speciation reactions in homoge-neous aqueous solutions and to characterize the struc-ture of mineral surfaces. The aqueous speciationdetermines which species will be present in solution,

while the mineral surface structure determines the sitegeometry and the electrical and chemical potentialavailable for the bonding of these aqueous speciesto the surface. The combination of surface structuralsites and homogeneous solution speciation leads tothe formation of a distinct set of surface species,each with specific chemical structure and reactivity,at the mineral surface.

In this article, equilibrium thermodynamics ofhomogeneous aqueous systems will be brieflyreviewed. Next, the characteristics of mineral surfaceswill be explored using information derived from crys-tal chemistry, spectroscopy and microscopy. With thisinformation in hand, empirical models of adsorptionreactions and more sophisticated surface complexa-tion models will be discussed. The latter modelsallow quantitative exploration of the effects of surfacespeciation and adsorbate structure on adsorbate reac-tivity, mineral dissolution rates and precipitationprocesses. Here, in particular, the relationshipbetween surface speciation and far-from-equilibriumdissolution kinetics will be reviewed. Finally, consid-eration will be given to the applicability of micro-scopic- or laboratory-scale studies of mineral–waterinteractions to field-scale systems.

2. Complexation in aqueous solution

Aqueous solutions consist of a polar, high dielectricsolvent (water) and chemical elements that aredissolved in that solvent. Dissolved elements innatural waters may be present in many differentforms, called chemical species, such as cations,anions, neutral molecules or complexes. Cations andanions in aqueous solution are solvated, meaning thatthey are surrounded by a hydration shell of watermolecules that form dipole–ion bonds with thedissolved ions. Cations and anions or other moleculesmay also coordinate (i.e. bond to each other) to formion-pairs or aqueous complexes, in which a centralmetal atom is surrounded by anions or moleculescalled ligands.

The terms ‘ion-pair’ or ‘outer-sphere complex’ aresometimes used to describe bonding between ions thatis due strictly to electrostatic interactions. In this typeof bonding, the hydration shells of the cation, anion,or both are retained. Stronger associations, termed

C. Koretsky / Journal of Hydrology 230 (2000) 127–171128

‘aqueous-complexes’ or ‘inner-sphere complexes’,may occur due to covalent attraction of a metal to aligand. In this case, the d-orbital electrons of the metalatom accept electron pairs (i.e. the metal acts as aLewis acid) from a ligand (the Lewis base) to forma covalent bond; each ligand replaces one of thehydration shell water molecules. Although the term‘complex’ is sometimes used to refer specifically tothis type of pairing, it is often used in a general senseto indicate either inner-sphere or outer-sphere typecomplexes, and that is the convention used in thispaper.

Natural waters contain a plethora of dissolvedcations and anions, both inorganic and organic; somany different species might be present in a given

solution. For example, in a solution with onlydissolved Mg, Cl and CH3COOH (acetate, anorganic ligand), all of the following aqueousspecies may be present: Mg12, Cl2, MgCl1, MgCl2,MgCl3

2, MgOH1, Mg(OH)2, CH3COO2 (acetate),MgCH3COO1 and Mg(CH3COO)2. The most abun-dant forms of a number of inorganic elements in typi-cal natural waters are shown in Table 1.

The actual form of dissolved elements is a matter ofgreat importance, particularly in studies of metaltransport, because of the increased solubility of metalsin the presence of aqueous complexes, and in biogeo-chemical studies, because the bioavailability andchemical reactivity of an element are primarily deter-mined by its speciation (Sunda and Guillard, 1976;Logan and Traina, 1993; Manahan, 1994; Campbell,1995; Deighton and Goodman, 1995). For example,‘bare’ or ‘free’ metal ions (i.e. ions that are presentonly as aquo-complexes) are typically much morebioavailable than complexed metals (see for exampleCampbell, 1995, Table 1). Thus, it is generally not thetotal concentration of a given metal in solution thatdetermines its availability as a nutrient (or as a toxin),but the concentration of the free aqueous ion. Thisconcept has been termed the ‘free ion activitymodel’ of bioavailability.

As an example, Allen et al. (1980) studied algalgrowth in media containing toxic levels of dissolvedzinc (4.8× 1027 M total Zn) both with and withoutvarious concentrations of a series of ligands. Theconditional stability constants of the chosen Zn-ligandcomplexes varied over nine orders of magnitude andthe concentrations of the ligands were varied overthree orders of magnitude. After 2 weeks of growth,the measured density of algal cells was observed tovary over four orders of magnitude. Nonetheless, asimple speciation calculation showed that the log ofthe number of cells present after a given growthperiod was inversely proportional to the concentrationof free Zn12

�aq� in all cases (Fig. 1).Although numerous studies of copper, cadmium

and zinc uptake by organisms suggest that the concen-tration of the free aqueous cation is the primary factorin determining bioavailability, it should be noted thatin a few cases other complexes or mechanisms mayalso play an important role. Campbell (1995) reviewsexceptions to the free ion activity model of bioavail-ability and points out that this model remains largely

C. Koretsky / Journal of Hydrology 230 (2000) 127–171 129

Table 1Principal forms of inorganic aqueous species in terrestrial naturalwaters (modified after Stumm and Morgan, 1996; Table 6.5)

Element Major species

B H3BO3, B�OH�24V HVO22

4 ; H2VO24

Cr CrO224

As HAsO224

Se SeO224

Mo MoO224

Si Si(OH)4Li Li 1

Na Na1

Mg Mg12

K K 1

Ca Ca12

Sr Sr12

Cs Cs1 2Ba Ba12

Be BeOH1, Be(OH)2Al Al �OH�12 ; Al �OH�24Ti Ti(OH)4

Fe Fe�OH�12 ; Fe�OH�24Co Co12, CoCO3

Ni Ni 12, NiCO3

Cu CuCO3, Cu(OH)2Zn Zn12, ZnCO3

Ag Ag1, AgClCd Cd12, CdCO3

La LaCO13 ; La�CO3�22

Hg Hg(OH)2Tl Tl 1, Tl(OH)3, Tl�OH�24Pb PbCO3

Bi Bi(OH)3

Th Th(OH)4U UO2�CO3�22

2 ; UO2�CO3�243

untested in solutions containing natural dissolvedorganic matter. Nonetheless, it is clear that a quanti-tative account of aqueous metal speciation is vital inunderstanding metal toxicity and nutrient availabilityin aquatic environments.

Metal speciation is also crucial in determining therates of chemical reactions in homogeneous solutions.For example, complexes of Fe(II) with humic-likeligands have been shown to stabilize Fe(II) withrespect to oxidation. Therefore, the kinetics of Fe(II)oxidation in aqueous solution depend not only on pHand fO2

; but also on the solution speciation of iron(Pankow and Morgan, 1981).

2.1. Equilibrium thermodynamics

Typically, the speciation of natural waters is notmeasured directly. Instead, total concentrations ofdissolved elements are measured and equilibriumthermodynamics are used to calculate the speciation(for much more detailed descriptions of equilibriumthermodynamics and speciation in geochemicalsystems see: Nordstrom and Munoz, 1986; Andersonand Crerar, 1993; Morel and Hering, 1993; Anderson,

1996; Stumm and Morgan, 1996; Drever, 1997). Atequilibrium, a given system will be in a state of mini-mum free energy; properties of the system will notchange over time, and the system will return to theminimum free energy state after slight disturbances.In general, geochemical systems are not in a state ofoverall, or ‘global’ equilibrium. However, it is veryoften true that subsets of reactions in the system occurrapidly enough that these reactions may be thought ofas achieving a state of ‘local’ equilibrium. In particu-lar, homogeneous aqueous solution reactions that donot involve electron transfer (i.e. those that do notinvolve oxidation/reduction) are often in local equili-brium, and so they may be modeled using equilibriumthermodynamics.

Although thermodynamic calculations cannot beused to ascertain the rates of chemical reactionssuch as speciation reactions, they can be used todescribe the state of the system once it has reachedequilibrium. For example, a metal–organic complexa-tion reaction might be written as

M12�aq� 1 L2

�aq� $ ML1�aq� �1�

where M12�aq� is a dissolved metal, L2�aq� the aqueous


Fig. 1. Growth ofMicrocystis aeruginosaafter 5 days as a function of free Zn concentration in the presence of varying concentrations ofnitrilotriacetic acid (NTA). Total concentration of Zn was 4:8 × 1027 M in all experiments. Data from Allen et al. (1980).

organic ligand, and ML1�aq� the aqueous metal–organiccomplex. Using thermodynamics, the concentrationsof ML1

�aq�; M12�aq� and L2

�aq� present at equilibrium can becalculated. In addition, if not at equilibrium, thechange in the Gibbs free energy associated with thereaction�DGr� can be used to predict the direction inwhich a chemical reaction will proceed to reachequilibrium: a negativeDGr indicates that the reactionwill proceed spontaneously in the direction written; apositiveDGr indicates that the reaction will proceedspontaneously in reverse.

DGr at a particular temperature and pressure isgiven by

DGr � DG8r 1 RT lnY

i

anii � DG8r 1 RT ln Q �2�

whereDG8r is the standard state change in the Gibbsfree energy of the reaction at the temperature andpressure of interest, R the universal gas constant,Tthe temperature,ai the activity of speciesi andn i itsstoichiometric coefficient (by convention, stoichio-metric coefficients are positive for products and nega-tive for reactants). The activity of a speciesi isessentially its “effective” concentration, and can becalculated from the relationship

ai � gimi

�gimi�8 �3�

where g i is the activity coefficient of i, mi themeasured concentration ofi and ‘8’ denotes the activ-ity coefficient and concentration of speciesi in thereference state. In an ideal solution, the activity of aspecies is equal to its concentration. Thus,g i can bethought of as a measure of the non-ideality of a solu-tion. In aqueous solutions most of the non-idealityarises from electrostatic interactions. Therefore, theactivity coefficients of solutes in very dilute solutionsor those of small, neutral molecules are generallyclose to one. Activity coefficients cannot be calculatedfrom thermodynamics, but can be calculated usingphysical models of molecular interactions, such asthe Debye–Hu¨ckel theory (Debye and Hu¨ckel,1954). For solutions of ionic strength.1021 M, activ-ity coefficients may be calculated using extendedversions of the Debye–Hu¨ckel equation, such as theDavies equation (Davies, 1962), the_B equation(Helgeson et al., 1981) or the Pitzer model (Pitzer,1987).

At equilibrium,DGr is equal to zero andQ is giventhe special name of equilibrium constant (K).Measured equilibrium constants (often called ‘stabi-lity constants’ for complexation reactions) have beentabulated for many aqueous complexation reactions(Sillen and Martell, 1964, 1971; Smith and Martell,1976). In addition, equilibrium constants have beenpredicted for many aqueous complexation reactions at258C and 1 bar, as well as at elevated temperaturesand pressures (Shock and Koretsky, 1993, 1995; Haaset al., 1995; Sverjensky et al., 1997; Shock et al.,1997; Xu and Wang, 1999). The equilibrium constant,which is a function only of temperature and pressure,can then be used to calculate the ratio of the activitiesof the product and reactant species that will be presentwhen a reaction is at equilibrium.

2.1.1. Aqueous speciation calculationsAs discussed above, the total concentrations of

dissolved chemical elements, rather than the concen-trations of individual aqueous species, are oftenmeasured, even though the distribution of species ina given solution might be of primary importance forpredicting the chemical and biological fate of theelements. By combining mass law expressions (Eq.(2)) with measured total concentrations of dissolvedelements, it is possible to calculate the equilibriumdistribution of individual aqueous species in a givensystem. The procedure for this type of calculation,called a speciation calculation, is explained in detailin a number of texts (e.g. Garrels and Christ, 1965;Anderson and Crerar, 1993; Morel and Hering, 1993).

Attempts have been made to assess uncertainties incalculated speciation resulting from uncertaintiesin measured data, as well as from imprecise orvaguely described thermodynamic data (Schecherand Driscoll, 1987, 1988; Nordstrom and Ball, 1984;Criscenti et al., 1996; Schulz et al., 1999). For exam-ple, Criscenti et al. (1996) propagated Monte Carlogenerated uncertainties in thermodynamic data and inmeasured concentrations of geochemical speciesthrough a speciation code to produce probabilisticdistributions of the calculated solution speciation.Fuzzy set theory has also been used to assess uncer-tainties in speciation calculations (Schulz et al.,1999). In this approach, the imprecise and vaguenature of thermodynamic datasets may be expressedin a non-probabilistic manner using fuzzy numbers.


These fuzzy numbers, representing the thermo-dynamic datasets, are then combined with probabilis-tic expressions of analytical uncertainties in measuredconcentrations of geochemical species to evaluate theeffects of each on calculated speciation. In a study ofcadmium and sulfur speciation, Schulz et al. (1999)concluded that in many cases the effects of impreciseand vague thermodynamic data probably far outweighanalytical uncertainties in the calculated speciation,pointing to a pressing need for improved thermo-dynamic datasets.

3. Mineral surface characterization

3.1. Crystal chemical description

To understand the complexation reactions that

occur at the mineral–water interface, it is importantto describe the substrate on which such reactionsoccur, i.e. the mineral surface. By definition, mineralsare composed of periodic three-dimensional (3D)crystal lattices (Klein and Hurlbut, 1993). However,at the mineral surface, the periodic array is termi-nated, leaving a surface with properties that may bequite different from those of the bulk 3D structure.Atoms at mineral surfaces are coordinatively unsatu-rated; that is, they are bonded to fewer atoms than theywould be if they were present in the bulk of themineral structure. Cations at the surface are left withan excess of positive charge because bonds to anionshave been severed in forming the surface, while coor-dinatively unsaturated anions are left with an excessof negative charge. In contact with air or with aqueoussolution, such coordinatively unsaturated cations andanions may hydroxylate or protonate, respectively, to


Fig. 2. (A) Schematic representation of a three-fold coordinatively unsaturated silicon atom with a partial positive charge at the surface of amineral such as quartz. (B) An isolated surface hydroxyl group is formed by the addition of a hydroxyl anion to the coordinatively unsaturatedsilicon atom depicted in (A). (C) Schematic representation of a two-fold coordinatively unsaturated oxygen atom with a partial negative chargeat the surface of a mineral such as a feldspar. (D) A bridging surface hydroxyl group is formed by protonation of the coordinatively unsaturatedoxygen atom depicted in (C).


Fig. 3. Experimentally determined site densities (per nm2) from the tritium exchange method and calculated site densities from Koretsky et al.(1998): (A) assuming that each broken bond at the surface of the mineral corresponds to one site or (B) using partial changes of coordinativelyunsaturated atoms at the surface to calculate site densities. Estimated site densities are indicated by filled circles for {100} planes, filled squaresfor {010} planes, filled diamonds for {001} planes, filled triangles for {110} planes, filled upside down triangles for {101} planes, open squareswith a cross for {011} planes, open squares with a hatch for {111} planes andx’s for {1 2 12} planes. The range of experimental and estimateddata for each mineral is indicated by a box.

form surface hydroxyl groups (Fig. 2). The latter mayreact with chemical species in aqueous solution togive rise to other types of surface complexes, andmay also act as sites for mineral dissolution and preci-pitation reactions. In addition, many surface hydroxylgroups are thought to be amphoteric (i.e. they mayprotonate or deprotonate) and give rise to charge atthe mineral surface. This charge depends on the pH ofthe solution; the pH for a given mineral at whichpositively and negatively charged sites balance togive a neutral surface is known as the pH of thepoint of zero charge (pHZPC).

Even on idealized slices through relatively simplecrystal structures many different kinds of coordina-tively unsaturated atoms may be present on a givensurface. For example, the quartz (SiO2) structurecontains only tetrahedrally coordinated silicon atomsand two-fold coordinated oxygen atoms. Consideringa perfectly level slice through a quartz crystal,depending on where the slice is made through thecrystal, either three- or two-fold coordinated Siatoms (missing bonds to one or two oxygen atoms,respectively) may be left at the surface, while coordi-natively unsaturated oxygen atoms will always beone-fold coordinated (Koretsky et al., 1998). Morecomplex mineral structures may have multiple cationsin multiple coordination states; this leads to a muchgreater variety of structural surface sites, even on asingle crystal surface. In addition, in most mineralstructures not all cation–anion bond lengths areequal (i.e. they are not of equalstrength), so twoequally coordinatively unsaturated atoms at thesurface may, in fact, not be chemically equivalent.This is very important in surface reaction models,because changes in chemical structure are likely tolead to changes in reactivity.

To quantify reactions that occur at mineral surfaces,information concerning both the types of surface sitespresent and the number of these sites per unit surfacearea (the site density) is needed. Crystal chemicalconsiderations have been used in a number of studiesto try to provide this type of information (Anderson etal., 1965; Morimoto et al., 1969; Jones and Hockey,1971; Yates, 1975; Barron and Torrent, 1996; Rustadet al., 1996; Koretsky et al., 1998). Because surfacesites may not be equivalent on different planes of amineral, overall site types and densities depend notonly on crystal structures, but also on crystal

morphologies. In general, mineral structures forcommonly occurring oxide and silicate minerals arewell known (e.g. Wyckoff, 1963, 1968). However,crystal morphology may vary strongly depending onthe formation environment of the mineral and onphysical or chemical weathering reactions (Zoltaiand Stout, 1984; Deer et al., 1993; Klein and Hurlbut,1993). For simplicity, most crystal chemical studies ofmineral surfaces (and in fact, most studies of indivi-dual mineral surfaces in general) focus on the mostcommonly occurring cleavage or growth planes of themineral. However, it should be kept in mind thatdescriptions of the mineral made in this way areonly approximations of what is present on real mineralspecimens.

It is generally assumed in crystal chemical studiesof surface functional groups that the mineral is trun-cated to form a smooth surface exactly parallel tocleavage or growth directions, and then the numberof each type of surface site is counted and categorized.Although this approach is conceptually quite simple,there does not seem to be any consensus as to whatconstitutes a ‘reactive surface site’. For example,assuming that each “near-surface” silicon atom onamorphous silica may function as one site, Iler(1979) estimated that there would be 7.85 OH/nm2.Boehm (1966), however, suggested that steric inhibi-tion would allow only half of these atoms to functionas reactive sites, and therefore predicted a site densityof 3.93 OH/nm2. In a recent study, Koretsky et al.(1998) used calculated bond strengths and chargesto find the “ideal” truncations of various crystalsand then used only these ideal surfaces to estimatesite types and densities, rather than considering arbi-trary slices through the crystal structure. Setting thenumber of broken bonds at the surface equal to thenumber of reactive surface sites, or considering partialcharges of coordinatively unsaturated atoms at thesurface, gave the best agreement with availableexperimentally determined site densities from tritiumexchange experiments (Fig. 3). In addition, the typesof surface hydroxyl groups predicted using thisapproach were in qualitative agreement with thoseobserved using surface infrared spectroscopy. Rangesof site densities from crystal chemical considerationsand from tritium exchange experiments for a varietyof silicate minerals are given in Table 2.

In all of the crystal chemical approaches discussed


above, it is implicitly assumed that mineral surfacesare ‘flat’, that is, that cleavage or growth planes areexactly parallel to a given direction. In fact, realmineral surfaces are not flat. Using statisticalmechanics, Burton et al. (1951) predicted that themost stable mineral surfaces would have complextopographies with spirals, steps and kinks. Sincethen, experimental evidence from studies using, forexample, atomic force microscopy, scanning tunnel-ing microscopy and scanning electron microscopy,have shown definitively that real minerals are nottopographically flat (e.g. Lasaga, 1990; Hochella,1990, 1995; Teng and Dove, 1997; Teng et al.,

1998). Both mineral growth and dissolution processesmay lead to such topographies. It has been shown bothin laboratory experiments (Grandstaff, 1978; Brantleyet al., 1986; Gratz et al., 1990) and on naturally weath-ered samples from the field (Berner and Holdren,1977, 1979; Banfield et al., 1995) that deep etch pitsmay form on mineral surfaces during dissolution.Furthermore, the density and morphology of suchpits may be controlled by the distribution of defectsin the mineral, as well as by solution compositionduring dissolution (Blum and Lasaga, 1987; Lee andParsons, 1995; Teng and Dove, 1997). Similarly,mineral growth does not generally lead to atomicallyflat surfaces, rather, very complex topographies mayresult, depending on the mechanism and rate ofmineral growth (Nielsen, 1984; Sunagawa, 1987;Christoffersen and Christoffersen, 1990; Zhang andNancollas, 1990).

3.2. Spectroscopic and microscopic evidence

Although considerations of crystal chemistry canbe useful in understanding mineral surfaces and reac-tive surface sites, much of what we know about thechemistry, structure and topography of mineralsurfaces comes from microscopic or spectroscopicmethods. Techniques such as Fourier transform infra-red (FTIR) spectroscopy, X-ray absorption spectro-scopy (XAS), X-ray photoelectron spectroscopy(XPS), Auger electron spectroscopy (AES), second-ary ion mass spectroscopy (SIMS), and scanningtunneling microscopy (STM), can provide data onthe chemical composition of mineral surfaces. Surfacemicrotopographies have been studied using STM,atomic force microscopy (AFM) and scanning elec-tron microscopy (SEM), while surface structures canbe studied with low energy electron diffraction(LEED), AFM and STM. A number of review articleshave been published summarizing the use of these andother microscopic and spectroscopic techniques instudying mineral surfaces (Hochella, 1988, 1990,1995; Brown, 1990; Brown et al., 1995, 1998;Greaves, 1995; Vaughan, 1995) and processes thatoccur at mineral surfaces. In the following section,examples of current research directions for one micro-scopic (AFM) and one spectroscopic (XAS) techniqueare explored.


Table 2Ranges in measured site densities (in sites/nm2) from the tritiumexchange method (Yates et al., 1977; Altmann, 1985; Hsi and Lang-muir, 1985) and calculated site densities (Koretsky et al., 1998)from crystal chemical considerations. pHZPCvalues from Sverjenskyand Sahai (1996)

Mineral (Formula) Plane Site density pHZPC

Quartz (SiO2) {100} 7.5{001) 9.6{110} 8.7{011} 5.9{111} 7.9Whole mineral 6.3–11.47 2.9

Hematite (Fe2O3) {100} 14.4–23.1{001} 4.5–27.3{112} 14.5Whole mineral 4.5–27.3 8.5

Corundum (Al2O3) {100} 16.2–25.9{001} 5.1–30.5{112} 16.4Whole mineral 5.1–30.5 9.4

Goethite (FeOOH) {100} 0–14.4{010} 8.7–17.4{001} 10.0–20.0Whole mineral 8.7–20.1 9.4

Rutile (TiO2) {100} 14.7{001} 14.2–19.0{110} 10.4{101} 15.9{111} 17.5–21.0Whole mineral 5–15.5 5.2

Periclase (MgO) Whole mineral 0–32.2 12.2Andalusite (Al2SiO5) Whole mineral 11.0–13.7 6.9Sillimanite (Al2SiO5) Whole mineral 13.2–18.5 4.9Sanidine (KAlSi3O8) Whole mineral 7.2 (6.1)a

Anorthite (CaAl2Si2O6) Whole mineral 5.3–11.5 5.6Albite (NaAlSi3O8) Whole mineral 3.8–11.5 5.2

a pHZPC for microcline.

3.2.1. Current directions in spectroscopic andmicroscopic techniques

3.2.1.1. Atomic force microscopy.The complexmicrotopographies of many mineral surfaces havebeen studied using AFM (Hochella, 1990, 1995;Gratz et al., 1991; Heaton and Engstrom, 1994;Liang et al., 1996; Teng and Dove, 1997; Teng etal., 1998; Fig. 4). Vertical changes in topographycan be measured at the A˚ -scale, while lateral resolu-tion is generally on the order of nanometers. AFM canbe used to study both insulating and conducting mate-rials. In addition, because AFM can be used to studysamples both in air and in aqueous solution, it can beused to observe changes in mineral topography asdissolution or precipitation reactions proceed (e.g.Fig. 4) or as mineral surfaces are contacted by bacteria(Grantham and Dove, 1996; Grantham et al., 1997).

Fundamental data describing the relationship

between equilibrium thermodynamics and calcitegrowth kinetics in the presence or absence of asparticacid has recently been collected using AFM (Teng etal., 1998). Teng et al. (1998) measured the velocityand critical length of steps growing at dislocations(Fig. 4) on calcite in solutions slightly supersaturatedwith respect to calcite. With these data, they were ableto provide the first experimental verification of theGibbs–Thompson relationship (Burton et al., 1951),a theoretical relationship describing the dependenceof step kinetics at growth spirals on equilibriumthermodynamics.

3.2.1.2. X-ray absorption spectroscopy.XAS holdsgreat potential for answering questions concerningthe geometrical details of adsorbed species (Brown,1990; Greaves, 1995; Brown et al., 1995). Two typesof spectra are produced in this technique, an X-rayabsorption near edge structure (XANES) spectrum


Fig. 4. AFM image of a growth spiral on calcite in a calcium chloride, sodium bicarbonate solution. Step heights are approximately 3 A˚

(micrograph courtesy of H. Teng and P. Dove).

and an extended X-ray absorption fine structure(EXAFS) spectrum. EXAFS spectra yieldinteratomic distances between the element ofinterest and its first and second nearest neighbors to^0.02 A and yield coordination numbers with theseneighbors within^15–20%. It should be noted,however, that this is a bulk technique, sointeratomic distances and coordination numbersrepresent an average of the various localenvironments within which the element occurs.XANES gives less quantitative information, but canalso provide information concerning the localstructural environment of the element of interestthrough comparison to spectra of well-characterizedsamples. Because XAS spectra can be measured onsamples in contact with air or with aqueous solutions,this technique has been used to measure bond lengthsand coordination numbers of adsorbed cations onvarious minerals (see for example: Manceau et al.,1992; O’Day et al., 1994a,b, 1996; Papelis et al.,1995; Bargar et al., 1996) and to distinguishadsorbed species from those present in solidmatrices (for example: Manceau et al., 1996),which can be difficult to do using macroscopictechniques.

Friedl et al. (1997) used XAS to study the cyclingof Mn minerals at the oxic/anoxic boundary of aeutrophic lake. They only found reduced Mn in thetop 2 mm of the lake sediments, indicating that reduc-tion reactions occurred at rates comparable to thesedimentation rate (2.5 mmol m22 d21). They werealso able to identify the two major forms of Mn inthis sediment sample; 55–60% of the Mn was asso-ciated with carbonate minerals, while 40–45% of theMn was incorporated into phosphate minerals. Asstressed in their study, XAS can be a useful tool forthe study of poorly crystalline, X-ray amorphousenvironmental samples, particularly if only one ortwo phases containing the element of interest arepresent in the sample.

4. Complexation at the mineral–water interface

The intricate topography of mineral surfaces, withtheir complex collections of reactive sites, allows avariety of chemical reactions to occur at the mineral–water interface. Reactions which involve uptake of

species from the aqueous solution in the presence ofa mineral are termed sorption, absorption or adsorp-tion reactions (for more details see the following text-books: Sposito, 1984, 1989; Dzombak and Morel,1990; Morel and Hering, 1993; Appelo and Postma,1996; Stumm and Morgan, 1996; Drever, 1997). In anabsorption reaction, a chemical species is removedfrom the aqueous solution and penetrates the crystallattice. The term adsorption is used if species aretaken up from the solution and are chemicallybound in a monolayer at the mineral–water interface.In other words, adsorbates (adsorbed chemicalspecies) remain within the essentially 2D mineral–water interface, in contrast to dissolved or solid chemi-cal species which exist in a 3D aqueous phase or solidlattice (Fig. 5). Adsorbed species are often shown inchemical reactions with symbols such as., . S orxwhich represent a bond to the underlying crystal struc-ture. For example, the adsorption of Cd12 from solutiononto a surface site (. S) might be written as

Cd12�aq�1 . S�. SCd12

: �4�

If the mechanism of uptake of a species from solution isunknown, the general term sorption may be used todescribe the reaction. In this paper, adsorption reactionswill be the primary focus.

Adsorbates may form different types of bonds withthe mineral surface. In physical adsorption or “physi-sorption”, the adsorbate is held at the surface only byrelatively weak van der Waals bonds. Electrostaticadsorption occurs due to the attraction of oppositecharges, as described by Coulomb’s law; the attractiveforce falls off with the square of the distance betweenthe two charged particles. In chemical adsorption,much stronger ionic or covalent (“chemical”) bondsform between the adsorbate and the surface site. Theterm “non-specific” adsorption is often applied tophysical or electrostatic adsorption, while chemi-cal adsorption is referred to as “specific” adsorp-tion.

It has been suggested that most non-specificallybound species form “outer-sphere” complexes at thesurface, in which the hydration sphere is retainedduring adsorption, whereas specifically bound speciesform “inner-sphere” complexes at the surface, losingpart or all of the hydration sphere in the adsorptionreaction (Fig. 6). Such complexes are often identified



Fig. 6. Schematic representation of inner-sphere and outer-sphere surface complexation. The Na atom is bonded to the surface oxygen atom asan outer-sphere complex, with a complete hydration sphere; the Fe atom has lost a part of its hydration sphere and forms an inner-sphere surfacecomplex.

Fig. 5. Schematic representation of the adsorption, absorption and precipitation of Zn on an iron oxide surface. All three processes are describedby the general term sorption.

based on evidence from bulk solution experiments.Because electrostatic attraction only occurs betweenoppositely charged ions, species observed to adsorbonly when the mineral surface holds an oppositecharge (i.e. cations that adsorb only at or above andanions that adsorb only at or below the point of zerocharge of a mineral) have been categorized as non-specifically adsorbed. In addition, decreased adsorp-tion with increasing ionic strength of inert backgroundelectrolytes has been taken as evidence of non-speci-fic adsorption (Sposito, 1984; Parks, 1990). Recently,X-ray absorption spectroscopy has been used to

distinguish inner- and outer-sphere complexes(O’Day et al., 1994a,b, 1996; Bargar et al., 1996;Thompson et al., 1997).

The question of whether a particular species isspecifically adsorbed as an inner-sphere complex ornon-specifically adsorbed as an outer-sphere complexis important because of the influence the type ofadsorption has on the structure and reactivity of theadsorbed species. Outer-sphere complexation causesminimal changes in the electron density distributionof the adsorbed species as compared to the aqueouscomplex. Because there is very little change in struc-ture as compared to the aqueous species, reactivity islikely to be comparable to that of the aqueous species.However, inner-sphere complexation leads tosubstantial alterations in the electron density distribu-tion (i.e. in structure), which may lead to significantchanges in reactivity.

4.1. Empirical/semi-empirical models of adsorption

4.1.1. Partition coefficientsAdsorption isotherms, which are simply equations

relating the equilibrium concentration of a speciesadsorbed on a given mineral to the concentration ofthat species in solution, are frequently used in empiri-cal or semi-empirical models of adsorption. One ofthe simplest of these is the distribution coefficient(Kd) model, which may be used to model the adsorp-tion of species present in solution in trace concentra-tions. Distribution coefficients are measured byimmersing a solid in a batch reactor containing a solu-tion with a known concentration of a given solute, A.After a given time, the concentration of A left in solu-tion is measured and a distribution coefficient isderived using the equation,

�. SA� � KdA�aq�; �5�where A(aq) is the concentration of A in solution and[ . SA] is the concentration of A that has adsorbed tothe mineral (Fig. 7A). Distribution coefficients areoften used to describe the adsorption of organicsonto mineral surfaces and to describe the cation oranion exchange capacities of clay minerals. In addi-tion, retardation of chemical species in soils and aqui-fers has been modeled frequently using distributioncoefficients, largely because they are easily incorpo-rated into advection–dispersion equations. However,


Fig. 7. Lines depict the form of empirical isotherms (concentrationsof adsorbed species,Cads, versus concentration of species in solu-tion, Csoln) calculated from: (A) the distribution coefficient model;(B) the Langmuir model; and (C) the Freunlich model.

Kd values are completely empirical, and as such, areapplicable only to the measured system. Changes insolution composition and speciation, choice ofmineral sample or pretreatment of the mineral sample(which may alter topography or composition of themineral surface), may change the measuredKd bymany orders of magnitude (e.g. Tessier et al., 1989;Staunton, 1994), which greatly limits the applicabilityof such coefficients to environmental systems, whichare often spatially and temporally heterogeneous. Forexample, Staunton (1994) measured distributioncoefficients for cesium in four soils of varying claymineralogy. He found that measured values ofKd

varied over approximately four orders of magnitudefor these soils and that the adsorption isotherm wasnot linear, even at surface concentrations of cesium aslow as 1026 mol Cs/kg soil. Fig. 8 illustrates thestrong dependence of measured logKd values as afunction of pH for Zn adsorbing on oxic lake sedi-ments (Tessier et al., 1989). Thus, a decrease in pH byonly half a log unit, from 7.5 to 7.0, changes the

measured logKd by nearly an order of magnitude,from approximately 2.8 to 1.9. To understand howthis relatively small change in pH would affect theconcentration of dissolved Zn12 in the sediment pore-waters, assume that the total concentration of Zn12

(that is, the concentration of sorbed Zn12 plus theconcentration of aqueous Zn12) is 100mM. In thatcase,

Kd � �. SZn12�Zn12�aq�

� �. SZn12��100mM 2 �. SZn12�� : �6�

Therefore, at pH 7.5, there would be 0.2mM Zn12

in solution. At pH 7.0 the concentration of Zn12 insolution would increase to 1.2mM. In other words, ifthe logKd measured at pH 7.5 was used to calculatethe concentration of Zn12

�aq� in a sediment at pH 7.0, thecalculated concentration of Zn12

�aq� would be too low bynearly an order of magnitude! Clearly, great caution iswarranted in using distribution coefficients to modeladsorption at pH values other than those for which


Fig. 8. Measured logKd (L/g) as a function of pH for Zn12 adsorbing on various oxic lake sediments. Data from Tessier et al. (1989).

coefficients have been measured. This is especiallysignificant in highly heterogeneous environments,such as aquifers, which may be sampled at one loca-tion to deriveKd values that are meaningless at thescale over which they are applied.

4.1.2. Langmuir and Freundlich isothermsThe equation for a Langmuir isotherm (Fig. 7B)

may be derived by assuming that: (1) all surfacesites are identical and have equal adsorption energiesand (2) adsorption occurs until a monolayer of adsor-bate forms at the mineral surface (Langmuir, 1918). Ifthere is only a single site at the surface and only oneadsorbate, A, then

Stot � �. S�1 �. SA� �7�where Stot is the total site density and [. S] theconcentration of bare surface sites. The adsorptionreaction may be written as

. S1 A�aq� $. SA �8�so that the equilibrium constant for reaction (8),KL, is

KL � { . SA}{ . S}{A �aq�}

�9�

where { } indicates activity. Combining Eqs. (7) and(9) yields the equation of a Langmuir isotherm,

{ . SA} � StotKL{A �aq�}

1 1 KL{ A�aq�}: �10�

Because this isotherm is derived assuming thatadsorption occurs at chemically equivalent surfacesites, adherence of experimental data to a Langmuirisotherm is sometimes taken as evidence for adsorp-tion at a single type of surface site. However, aspointed out by Sposito (1984), adherence of experi-mental solute uptake data to any isotherm does notimply that the mechanism of uptake is adsorption(rather than absorption or precipitation), nor doesadherence to a Langmuir isotherm constitute evidenceof a single adsorption site at the mineral surface. Forexample, mineral precipitation data may also adhereto the Langmuir isotherm (Veith and Sposito, 1977).

For trace concentrations of adsorbate A, the Lang-muir isotherm is linear and equivalent to using adistribution coefficient. In general, a Langmuirisotherm may provide a better description of

adsorption over larger solute concentrations than thesimpler, linearKd. In addition, the Langmuir isothermaccounts explicitly for the finite number of sites avail-able in a given mineral–water system. However, liketheKd, Langmuir adsorption constants depend on thechoice and treatment of mineral specimens and theyare a function of solution composition.

The Freundlich isotherm (Freundlich, 1909) isgiven by

�. SA� � KF�A�aq��n �11�wheren is a constant between 0 and 1 andKF is theFreundlich adsorption constant (Fig. 7C). Thisisotherm is frequently used to model adsorption onsolids with multiple types of surface sites or onheterogeneous solids, such as soils (Sposito, 1984).The Freundlich isotherm can be used to simulatesequential filling of surface sites with progressivelydecreasing adsorption energies. As shown by Sposito(1984), the Freundlich isotherm is equivalent to takingthe integral of a continuum of Langmuir isothermswith a normal distribution of adsorption constants.Like the Langmuir isotherm, the Freundlich isothermcan frequently be used to model adsorption over largerconcentration ranges of A than the simplerKd model.However, measured Freundlich adsorption constantsare also system dependent and are a function ofmineral sample and solution composition.

Isotherms are of limited use in describing geochem-ical systems with changing solution or mineral chem-istry. This is because they do not account explicitly forthe development of electrical charge on mineralsurfaces with the addition (or removal) of surfacespecies. Furthermore, these models do not includeany structural information regarding adsorbedspecies. Because the structure of an adsorbed specieslargely determines its reactivity, this is particularlylimiting when a species may adsorb at a mineralsurface with different structures, depending on solu-tion or mineral surface conditions.

4.1.3. Ion exchangeThe adsorption isotherms discussed above are

generally used to describe the adsorption of a singleion onto a given substrate. However, in most naturalenvironments adsorption at the surface is ‘competi-tive’, particularly with regard to major cations andanions. In other words, different types of dissolved


ions present in natural solutions ‘compete’ to adsorbat a limited number of sites on the substrate. In thesimplest case, competition among dissolved ions foradsorption may be described as an ion exchangeprocess, in which one adsorbed ion and one ion inthe aqueous phase trade places. For example, a K1

ion in aqueous solution may displace an adsorbedNa1 ion through the reaction

. S–Na1 K1�aq� $. S–K1 1 Na1

�aq�: �12�It can be seen with Eq. (12) that ion exchange is not adifferent process than adsorption, as is sometimessuggested, but is actually a coupled set of adsorptionand desorption reactions. In ion exchange reactions,adsorption is generally assumed to be non-specific,such that cation adsorption only occurs on negativelycharged surfaces (i.e. above the pHZPC) and anionadsorption only occurs on positively charged surfaces(i.e. below the pHZPC).

Ion exchange reactions are characterized by condi-tional equilibrium constants, sometimes calledexchange or selectivity coefficients. For example,the exchange coefficient of K1 for Na1 associatedwith Eq. (12) is given by

KK=Na �{ . SK1}{Na 1

�aq�}{ . SNa1}{K 1�aq�}

�13�

where { } indicate activity of the adsorbed or aqueousions. Ion exchange reactions may be added(subtracted) and their corresponding exchange coeffi-cients multiplied (divided) to calculate exchangecoefficients for different sets of ions. In addition, ionexchange coefficients can be used to determine therelative proportions of three or more non-specificallyadsorbed ions at the surface (see Appelo and Postma,1996) or to derive simple distribution coefficients for agiven element present in trace concentration in a solu-tion with constant concentrations of all other ions.However, like distribution coefficients or Langmuirand Freundlich isotherm models, the ion exchangemodel does not account for pH dependent surfacecharge or the structure of the substrate, and thus isof limited use in heterogeneous environments.

4.2. Surface complexation models

Many of the shortcomings of the isotherm or ionexchange approaches to modeling adsorption may be

overcome by explicitly representing the chemicalstructure of the mineral–water interface, as is donein ‘surface complexation models’ (SCMs). SCMs,which are based on thermodynamics and which areanalogous to aqueous speciation models, are a power-ful approach to surface reaction modeling (for moredetailed descriptions of SCMs see: Sposito, 1984,1990; Davis and Kent, 1990; Dzombak and Morel,1990; Morel and Hering, 1993; Schindler, 1990;Stumm, 1992; Stumm and Morgan, 1996). SCMsrepresent an improvement over empirical modelsof adsorption because the ‘intrinsic’ equilibriumconstants (K int) derived from SCMs are much lesssystem-dependent than those derived from empiricalmodels. Values ofK int depend only on the identity ofthe solid and the adsorbing solute (and for somemodels, on ionic strength), but do not depend on thepH, concentration of adsorbate or the solution compo-sition. Many different SCMs have been developed;only the most commonly used of these will be consid-ered here.

As emphasized by Dzombak and Morel (1990), allSCMs share at least four common characteristics.First, it is assumed that mineral surfaces can bedescribed as flat planes of surface hydroxyl sites andthat equations can be written to describe reactions atthese specific sites. So, for example, a surface proto-nation reaction might be written as,

. SOH1 H1�aq� $. SOH1

2 : �14�The second assumption common to all SCMs is thatreactions at mineral surfaces may be described usingmass law equations; in other words, these reactionsare assumed to be in a state of local equilibrium. Forreaction (14), the associated mass law equation is,

K int � { . SOH12 }

{ . SOH}{H 1aq}

�15�

where { } indicates activity of the species in brackets.Examples of mass law equations associated withprotonation, deprotonation, metal and ligand sorptionreactions are given in Table 3.

The third assumption adopted in all SCMs is thatvariable charge at the mineral surface is the directresult of chemical reactions at the surface. It hasbeen observed that minerals have zero surface chargeat a particular pH, termed the pHPPZC, or pH of the


pristine point of zero charge, which is a predictablefunction of mineral structure (Sverjensky, 1994).Titration of the mineral surface to a pH below thepHPPZC will result in a positively charged mineralsurface, whereas titration to a pH above the pHPPZC

will result in a negatively charged mineral surface,due to reaction of H1 or OH2 with surface hydroxylgroups (first two reactions in Table 3). This type ofvariable charge due to reactions at the surface isgenerally described in SCMs using an electric doublelayer model. (There may also be a component ofsurface charge associated with the structure of themineral, termed the ‘permanent’ charge, especiallyfor clay minerals. However, this charge will be aconstant, unaffected by surface complexation reac-tions.) In the electric double layer model, the chargeat the surface is balanced by a ‘diffuse layer’ ofcounterions in solution, near the charged mineralsurface. The separation of charge between these twolayers gives rise to an electric potential,c , which is afunction of the distance,x, from the surface. The

existence of this electric double layer, and its treat-ment in SCMs is what truly distinguishes them fromaqueous speciation models.

Finally, it is assumed in SCMs that the effect ofsurface charge on measured equilibrium constantsKapp

(or ‘apparent’ equilibrium constants), can be calculatedand the intrinsic equilibrium constants may then beextracted from experimental measurements. Thisseparation of intrinsic constants from measuredconstants is typically made using an ‘electrostatic’ or‘Coulombic’ correction factor of the form,

exp2zFc�x�

RT

� ��16�

wherez is charge,F the Faraday constant,c (x) theelectric potential as a function of the distancex fromthe surface, R the universal gas constant, andT thetemperature. Therefore,

K int � Kapp exp2zFc�x�

RT

� ��17�


Table 3Examples of adsorption reactions at the mineral–water interface with associated mass law expressionsa

Reaction Mass law expression

Protonation . SOH1 H1aq,. SOH1

2 K int1 � { . SOH1

2 }{ . SOH}{H1

aq}

Deprotonation . SOH,. SO2 1 H1aq K int

2 �{ . SO2}{H 1

aq}

{ . SOH}

Monodentate metal adsorption . SOH1 M1aq,. SOM1 H1

aq K intM;m �

{ . SOM}{H 1aq}

{ . SOH}{M 1aq}

Bidentate metal adsorption 2. SOH1 M1aq,. �SO�2M2 1 2H1

aq K intM;b �

{ . �SO�2M}{H 1aq}

2

{ . SOH}2{M 1aq}

Monodentate ligand adsorption . SOH1 L2aq,. SOL22 1 H1

aq K intL;m �

{ . SOL22}{H 1aq}

{ . SOH}{L 2aq}

Bidentate ligand adsorption 2. SOH1 L2aq,. �SO�2L23 1 2H1

aq K intL;b �

{ . �SO�2L23}{H 1aq}

2

{ . SOH}2{L 2aq}

a Notes: (1) The ‘aq’ subscript is sometimes replaced by the subscript ‘s’, to denote the concentration of aqueous H1 at the mineral–waterinterface, which in not in general equivalent to the bulk concentration of H1 due to electric field effects at the surface. (2) Brackets, { }, indicateactivity of the species. Because activity coefficients are typically assumed to equal one for surface species, mass law expressions are sometimeswritten in terms of the concentrations of surface species, rather than in terms of their activities.

whereKapp is the measured equilibrium constant for agiven set of solution conditions. Although theCoulombic correction factor is sometimes describedas an activity term (e.g. Dzombak and Morel, 1990), itis, in fact, a result of the electrochemical work,W,associated with moving a point charge,z, from aninfinite distance to a distance,x, from a chargedinfinite plane, such that

W � zFc�x� �18�(Sposito, 1990; Sverjensky and Sahai, 1996).

Differences between SCMs arise primarily from thedescription of the electric double layer, calculation ofthe electric potential,c , and from treatment of surfacesites as being either completely homogeneous (single-site models) or as being heterogeneous (multi-sitemodels). Characteristics of three of the mostcommonly employed models are summarized in Fig.9 and in Table 4.

4.2.1. MUSIC modelIn most applications of surface complexation

models, surface hydroxyl groups for a given mineralare assumed to be completely homogeneous (i.e. asingle-site model is used). Even for relatively simpleoxide minerals, however, it is clear that many types ofsurface hydroxyl groups may be present on a singleplane of the mineral, and that the reactivities of thesevarious types of surface groups are unlikely to be thesame. In single-site surface complexation models,differences in surface hydroxyl site reactivities areaveraged into the equilibrium constants. This limitsthe applicability of such constants to minerals withdistributions of sites similar to those used in theexperiments from which the equilibrium constantswere derived (i.e. to minerals of similar morphologyand surface composition).

To account for the varying reactivities of differenttypes of sites, multi-site surface complexation models,such as the MUSIC model developed by Hiemstra etal. (1989a,b), have been proposed. In this model,surface groups have been divided into six types:singly, doubly or triply coordinated surface oxygenatoms that may bond to either one or two surfaceprotons (Fig. 10). Although this description of sitetypes is still a great oversimplification, it is animprovement over homogeneous single-site models.The difficulty with the MUSIC model (and with all


Fig. 9. General form of the electric potential (C) versus distance (x)from the surface for: (A) the constant capacitance model; (B) thediffuse layer model; and (C) the triple layer model. In the CCM, aspecifically adsorbed plane of ions at the surface (xo) gives rise to acharge at the surface that is counterbalanced by a single plane ofcounterions at a distancexD from the surface. In the DLM, specificadsorption at the mineral surface plane is counterbalanced by adiffuse ion “swarm”, rather than simply by a plane of counterions.In the TLM, adsorption occurs on two separate planes (atxo andxb)with a diffuse ion “swarm” providing charge balance.

C.

Ko

retsky

/Jo

urn

alo

fH

ydro

log

y2

30

(20

00

)1

27

–1

71

145

Table 4A brief summary of features of three surface complexation models: the constant capacitance model (CCM), the diffuse layer model (DLM) and the triple layer model (TLM)a

Model Charge–electical potentialequation

Fit parameters Advantages Disadvantages References

CCM s0 � CCCMc0 CCCM, K1, K2 Few fitting parameters DerivedK1, K2 are afunction of ionicstrength andbackground electrolyte

Schindler and Kamber(1968), Hohl and Stumm(1976)

DLM sD � 20:1174��Ip

sinhzFcD

RT

� �from Gouy–Chapman theory

K1, K2 Few fitting parameters;K1, K2

are not a function of ionicstrength

DerivedK1, K- are afunction of backgroundelectrolyte

Stumm et al. (1970), Huangand Stumm (1973),Dzombak and Morel (1990)

TLM s0 � CTLM ;innerc0;

sb � Couter;TLMcb;

sD � 20:1174��Ip

sinhzFcD

RT

� �Cinner,TLM,Couter,TLM, K1,K2, KM, KL

Adsorption of ‘inert’ backgroundelectrolyte may be accounted forexplicitly; K1, K2, KM, KL arenot functions of ionic strength orsolution composition

Large number of fittingparameters

Yates et al. (1974), Davis etal. (1978), Hayes et al.(1991)

a CCCM, Cinner,TLM, Couter,TLM: capacitances for CCM model, the inner layer in the TLM model and the outer layer in the TLM model, respectively;K1, K2: intrinsic equilibriumconstant for protonation and deprotonation, respectively;KM, KL: intrinsic equilibrium constant for electrolyte cation and anion adsorption, respectively;s0, sD: charge at themineral surface and at the inner edge of the diffuse layer;c0, cD: potential at the mineral surface and at the edge of the diffuse layer;I: ionic strength;z: ion charge;F: Faraday’sconstant; R: universal gas constant;T: temperature.

multi-site models) comes in the large number of fittingparameters required to use experimental data toextract equilibrium constants for each type of reactionat each type of surface group. Hiemstra et al.(1989a,b) avoided this problem by using correlationalgorithms to predict equilibrium constants for eachtype of site. Their correlations are based on thenumber of M–O bonds in each surface hydroxylgroup, the Pauling bond strengths associated withthose bonds and the equilibrium constants for proto-nation of homogeneous aqueous solution complexesanalogous to the surface complexes. Hiemstra et al.(1989b) used the MUSIC model to model surfacecharge as a function of pH on various planes onoxide and hydroxide minerals and found that forsome of these minerals (e.g. gibbsite), surface chargedevelopment was very different for the differentplanes.

4.2.2. Comparison of model performanceSome effort has been made to compare the success

of the single-site constant capacitance, double andtriple layer models in modeling surface titration,surface charge and adsorption data for various puresolids. Davis and Kent (1990) reviewed some of thesecomparisons and concluded that all three of thesemodels are equally successful at modeling ion adsorp-tion in simple systems. Hayes et al. (1991) performedan extensive sensitivity analysis of the three models,testing the ability of each to represent surface titrationdata over ionic strengths of 0.001 to 0.139 M on rutile(TiO2), corundum (a-Al 2O3) and goethite (a-FeOOH). They treated the following as fitting para-meters in their analyses: site density (NS), K1, K2 andCCCM for the CCM;NS, K1 andK2 for the DLM; andNS, K1, K2, C1, C2, KM andKL for the TLM. Hayes etal. were able to fit the titration data using any of the


Fig. 10. Schematic representation of (A) singly, (B), doubly and (C) triply coordinated surface oxygen atoms on goethite used in the multi-sitesurface complexation model of Hiemstra et al. (1989a,b). (A) Singly coordinated oxygen atoms assigned a partial charge of21/2 were assumedto protonate to form isolated surface OH groups with a partial charge of11/2. (B) Doubly coordinated oxygen atoms assigned a partial chargeof 21 were assumed to singly protonate to form a neutral isolated surface OH group or doubly protonate to form an OH2 group with a charge of11. (C) Triply coordinated oxygen atoms assigned a partial charge of21/2 were assumed to protonate to form isolated surface OH groups witha charge of11/2.

SCMs with NS between 1 and 100 sites/nm2, butthe derived equilibrium constants depend on thevalue of NS used in the model. Although all threemodels could be used to fit surface titration data forthe three solids, Hayes et al. found that the TLM gavethe best fit to the data over wide ranges of ionicstrength for a single set of equilibrium constants.However, they also emphasized the advantage of theDLM in requiring fewer fitting parameters to modelthe data.

As discussed by both Davis and Kent (1990) andHayes et al. (1991), the main obstacle to application ofany surface complexation model does not reside intheir failure to provide adequate fits to experimentaldata. Rather, the major difficulty is the lack of consis-tent parameters (site densities, capacitances and equi-librium constants) for use with the models. Foradsorption on hydrous ferric oxide, this problem hasbeen largely remedied by the internally consistentDLM database developed by Dzombak and Morel(1990). Recently, Sahai and Sverjensky (1997a,b)and Sverjensky and Sahai (1996) have also developedinternally consistent sets of CCM, DLM, and TLMsurface equilibrium constants for protonation anddeprotonation, as well as TLM equilibrium constantsfor sorption of electrolyte ions on a variety of oxideand hydroxide minerals.

4.2.3. Measurement and estimation of surfacecomplexation model parameters

The use of any surface complexation modelrequires a large number of parameters, including sitedensities and surface areas for the solid, equilibriumconstants for protonation, deprotonation and adsorp-tion reactions, and, depending on the surfacecomplexation model used, one or more capacitancevalues. A variety of methods have been used to eithermeasure or estimate these parameters for systems ofinterest.

Site densities may be estimated based on crystalchemical considerations if measured values are notavailable. Site densities have also been measuredexperimentally for a limited suite of oxide and silicateminerals using methods such as tritium exchangemeasurements, surface titration experiments andinfrared spectroscopy (see James and Parks, 1982;Koretsky et al., 1998 for reviews of measured sitedensities). Because the site densities of relatively

few minerals have been measured using any of thesetechniques and because measured site densities varydepending on measurement technique and samplepretreatment conditions, site densities are frequentlyset equal to a constant (e.g. 10 sites/nm2), regardlessof the mineral actually being modeled. This maycause difficulties in comparing equilibrium constantsderived for minerals that actually have quite differentsite densities (Koretsky et al., 1998). Additional diffi-culties arise in characterizing systems such as soils orsediments that are composed of a mixture of minerals.Surface titration methods are difficult to apply to suchsystems, due to dissolution of phases and to slowequilibration (e.g. Bolt and Van Riemsdijk, 1987),and infrared spectroscopic or tritium exchange char-acterizations of site densities for mixed phases arecurrently lacking.

To calculate the number of reactive sites present ina given system from site densities, estimates of themineral surface areas are required. The simplestmethod for estimation of surface area is derivedfrom geometrical considerations; for example, parti-cles may be assumed to have a uniform sphericalshape and size. Surface morphologies may alsobe studied using scanning electron microscopy, andthe particle sizes and morphologies used to calcu-late the surface area. Because geometric estimationmethods are difficult to apply to most minerals,which may have very complex morphologies, inertgas adsorption data are usually used to measuremineral surface areas. In the Brunauer–Emmett–Teller (BET) method, the amount of N2, Kr orAr sorbed on the mineral as a function of the relativepartial pressure of adsorbing gas is measured and usedto calculate the surface area (Brunauer et al., 1938).Reactive surface areas for field-scale calculations aregenerally difficult to assess, requiring estimates of thereactive surface area per volume (m2 m23) over largeareas.

The CCM requires one capacitance value, while theTLM model requires both an inner- and an outer-layercapacitance, which are often treated simply as fittingparameters (e.g. Hayes et al., 1991). Hayes et al.(1991) found that a range of inner-layer capaci-tance values could be used to model surface titrationdata using the TLM; different values of the capaci-tance simply changed the values of the fitted equili-brium constants. Therefore, they suggested that the


capacitance values for the TLM and the CCM be setto constants. For the CCM, Hayes et al. (1991) suggesta capacitance of 1.0 F/m2, and for the TLM theysuggest setting the inner-layer capacitance equal to0.8 F/m2 and the outer-layer capacitance equal to0.2 F/m2. Sahai and Sverjensky (1997b) found arough correlation between inner-layer TLM capaci-tance values and the effective electrostatic radii andaqueous solvation coefficients of the aqueous electro-lyte. They used this correlation to predict inner-layercapacitances for a variety of aqueous electrolytes(Fig. 11).

The CCM, DLM, and TLM all require surfaceprotonation and deprotonation equilibrium constantsin addition to equilibrium constants for adsorption ofother species from solution, and the TLM alsorequires electrolyte metal and ligand adsorptionconstants. Usually, equilibrium constants are calculated

by fitting titration and adsorption data (e.g. Hayeset al., 1991). Recently, Sverjensky and Sahai (1996)developed correlation algorithms based on the inverseof the dielectric constant of the solid and the averagePauling bond strength in the solid to predict surfaceprotonation and deprotonation equilibrium constantsfor use with the CCM, DLM and TLM (Tables 5–7)Sahai and Sverjensky (1997b) have also developedmethods to predict electrolyte adsorption equili-brium constants for the TLM, based on the inverseof the dielectric constant for the solid, the chargeof the electrolyte ion, the effective radius of theadsorbed electrolyte ion and the electrostatic radiusof the electrolyte ion in aqueous solution. Rustadet al. (1996) have used molecular statics calcula-tions to predict surface protonation constants ongoethite for use with a multi-site surface complexa-tion model.


Fig. 11. Correlation for prediction of inner-layer triple layer model capacitances from Sahai and Sverjensky (1997b). Inner-layer capacitanceswere derived by fitting experimented surface titration data and are plotted against 1=�vre;j �ML wherevML is the aqueous Born coefficient of theelectrolyte andre,j,ML is the electrolyte effective electrostatic radius. Data indicated by filled circles were used to derive the correlation line ofC1 � 232:9 × 1=�vre;j �ML 1 5:9 given by Sahai and Sverjensky (1997b); data indicated by open triangles were excluded from the regression.

4.2.4. Application of surface complexation models tonatural systems

Application of surface complexation models tonatural solids such as sediments or soils is greatlyhampered by the dearth of parameters such as sitedensities, reactive surface areas and surface stabilityconstants for such materials and by the difficultiesassociated with estimating or measuring such para-meters on complex solids. Nonetheless, a number ofattempts have been made to use surface complexationmodels to describe adsorption onto complex naturaland anthropogenically produced materials, includingsediments and municipal waste incinerator bottom ash

(e.g. Osaki et al., 1990a,b; Fu and Allen, 1992; Vander Hoeck and Comans, 1996; Fuller et al., 1996;Wang et al., 1997; Davis et al., 1998; Meima andComans, 1998; Wen et al., 1998). In addition, surfacecomplexation modeling has been used successfully todescribe adsorption of metals onto bacterial cell walls(Fein et al., 1997; Daughney et al., 1998).

Surface complexation approaches to modelingmixed phases generally fall into two categories:generalized composite methods or component addi-tivity approaches (Davis et al., 1998). In the general-ized composite method, the mixed phase is treatedusing average parameters derived for the specificmaterial being studied, whereas in the componentadditivity approach, the components and the relativeabundances of pure phases contributing to the mixedphase must first be characterized, and then surfacecomplexation parameters independently derived forthe individual pure phases are used to model adsorp-tion on the complex material. The generalized compo-site method requires much less information than thecomponent additivity approach; however, apparentstability constants derived using this approach onlyapply to the sample studied. In addition, results areonly strictly applicable for solutions that are reason-ably close in composition to those used to derive theapparent stability constants because the effect ofcompetitive adsorption by other metals is not expli-citly accounted for in this model.

The generalized composite and component additiv-ity methods were compared by Davis et al. (1998) in astudy of Zn12 adsorption onto sandy aquifer sedi-ments using a non-electrostatic surface complexationmodel. They found that both approaches could beused to model their experimental data, however, thecomponent additivity approach could not be usedwithout adjusting surface area or site density para-meters. They concluded that application of thecomponent additivity approach could be greatlyimproved if more information pertaining to surfacecoatings were available from, for example, spectro-scopic characterizations of the sediments. Althoughthe two-site generalized composite approach requiredthree fitting parameters and is only strictly valid forthe measured sediments, Davis et al. (1998) demon-strated that it is nonetheless a great improvement overa distribution coefficient model because the derivedstability constants could be used over a range in pH


Table 5Predicted constant capacitance model parameters from Sverjenskyand Sahai (1996) using a site density of 10 sites/nm2 and a capaci-tance of 1.0 F/m2

Solid Ionic strength (M) logK1a log K2b

Goethite 0.001 6.6 211.10.01 6.9 210.70.1 7.3 210.3

Corundum 0.001 6.3 211.10.01 6.7 210.70.1 7.1 210.3

Ferrihydrite 0.001 6.6 211.10.01 6.9 210.70.1 7.3 210.3

Gibbsite 0.001 6.6 211.30.01 7.0 210.90.1 7.4 210.5

Rutile 0.001 2.5 29.30.01 3.1 28.70.1 3.6 28.2

Quartz 0.001 23.3 29.30.01 22.4 28.40.1 21.5 27.5

Silica 0.001 22.8 29.80.01 21.9 28.90.1 21.0 28.0

Albite 0.001 0.6 29.80.01 1.2 29.10.1 1.9 28.4

a Stability constant for the protonation reaction:.SOH1 H1

�aq� �. SOH12 :

b Stability constant for the deprotonation reaction:.SOH�. SO2 1 H1

�aq�:

(from 4.5 to 6.5) whereKd would vary over at leastthree orders of magnitude (see Fig. 8).

A number of other surface complexation studies ofadsorption onto natural sediment have beencompleted using a generalized composite approach.For example, in a study of copper and cadmiumadsorption onto natural river sediments, Wen etal. (1998) compared three of the commonly used

surface complexation models, the CCM, theDLM and the TLM, and found that all threecould be used with a one-site approach to repre-sent measured adsorption data. Fu and Allen(1992) used a multi-site surface complexationmodel to successfully model cadmium adsorptiononto natural sediments over a pH range of4.5–7.


Table 6Double layer surface complexation model parameters

Solid Cation/anion logK1a

Protonationlog K2b Deprotonation log K metal or ligandd

Goethite 7.5c 210.2c

Corundum 7.3c 210.2c

Ferrihydrite 7.5c 210.2c

Ba12 7.3d 28.9d 5.5e

Sr12 7.3d 28.9d 26.6f, 5.0e, 217.6g

Ca12 7.3d 28.9d 5.0e, 25.9f

Ag1 7.3d 28.9d 21.72h

Co12 7.3d 28.9d 20.46h, 23.0f

Ni12 7.3d 28.9d 0.37h

Cd12 7.3d 28.9d 0.47h, 22.9f

Zn12 7.3d 28.9d 0.99h, 22.0f

Cu12 7.3d 28.9d 2.9h

Pb12 7.3d 28.9d 4.7h

Hg12 7.3d 28.9d 7.8h, 26.5f

SO224 7.3d 28.9d 7.8i, 0.79k

SeO224 7.3d 28.9d 7.7i, 0.80k

SeO223 7.3d 28.9d 12.7i, 5.2k

S2O223 7.3d 28.9d 0.49k

CrO224 7.3d 28.9d 10.9i

PO234 7.3d 28.9d 31.3j, 25.4l, 17.7m

AsO234 7.3d 28.9d 29.3j, 23.5l

Gibbsite 7.5c 210.4c

Rutile 3.7c 28.2c

Quartz 21.6c 27.6c

Silica 21.1c 28.1c

Albite 1.9c 28.5c

a Protonation reaction:. SOH. H1�aq��. SOH1

2 :b Deprotonation reaction:. SOH�. SO21H1

�aq�:c From Sverjensky and Sahai (1996) using 10 sites/nm2.d From Dzombak and Morel (1990) using 0.056 high affinity sites/nm2 and 2.3 total sites/nm2.e Divalent metal adsorption on high affinity sites:. SOH1 M12�. SOHM12

:f Divalent metal adsorption on weak affinity sites:. SOH1 M12�. SOM11H1

:g Divalent metal adsorption on weak affinity sites:. SOH1 M121H2O�. SOMOH1 2H1

:h Divalent metal adsorption on high affinity sites:. SOH1 M12�. SOM11H1 or monovalent adsorption on high affinity sites:

. SOH1 M1�. SOM1 H1:

i Divalent ligand adsorption:. SOH1 L221H1 �. SL21H2O:j Trivalent ligand adsorption:. SOH1 L23 1 3H1�. SH2L 1 H2O:k Divalent ligand adsorption:. SOH1 L22�. SOHL22

:l Trivalent ligand adsorption:. SOH1 L23 1 2H1�. SHL21H2O:

m Trivalent ligand adsorption:. SOH1 L231H1�. SL221H2O:

In other studies of natural sediments, attempts havebeen made to correlate derived apparent stabilityconstants with properties of the adsorbate and/or theadsorbent. For example, Wang et al. (1997) used aDLM to fit apparent stability constants for copper,zinc, lead and cadmium adsorption onto 11 naturalsediment samples. They found a relationship betweenfitted apparent stability constants and first hydrolysisconstants of the adsorbates, and furthermore, that thiscorrelation was a function of sediment composition(percent total organic carbon and percent iron, manga-nese and aluminum oxides), suggesting that apparentstability constants might be predicted using sedimentcomposition data. Fuller et al. (1996) used a non-elec-trostatic surface complexation model to derive appar-ent stability constants for lead and zinc adsorptiononto aquifer sediments and found a relationshipbetween those constants and extracted iron andaluminum concentrations normalized to surface area,suggesting that easily measured properties of the sedi-ment might be used to give a qualitative indication ofapparent adsorption stability constants.

Currently, incorporation of surface complexationmodels into reaction transport models is fairly limited.This is probably due, at least in part, to the paucity ofsurface complexation model parameters presentlyavailable in the literature. As such parameters arereported for a wider range of adsorbates andminerals, inclusion of surface complexation modelingapproaches into sophisticated reaction transportmodels is likely to become more common (e.g.Wang and Van Cappellen, 1996).

4.3. Reactivity at the mineral–water interface

4.3.1. Contaminant degradation and immobilizationThe mobility and degradation of both organic

and inorganic contaminants may be stronglyaffected by adsorption to mineral surfaces andby subsequent surface reactions. Surface reactionsmay enhance organic hydrolysis reactions (Stone,1989a,b; Torrents and Stone, 1991; Larson andWeber, 1994), inhibit (e.g. Weber and Wolfe,1987) or enhance (e.g. Dragun and Helling,1985; McBride, 1987; Klausen et al., 1995) reduc-tive or oxidative organic degradation reactions,and enhance inorganic oxidation and reduction

reactions (e.g. Sørensen and Thorling, 1991;Manning and Goldberg, 1997; Liger et al., 1999).

Quantifying enhanced organic reduction ratesdue to surface reaction is of particular interest inthe study of contaminants, which may come intocontact with a wide variety of mineral surfaces,and which may have reduction products that aremore toxic than the reactants themselves. Forexample, Klausen et al. (1995) measured rates ofreduction for a series of substituted nitrobenzenesin the presence or absence of Fe(II)- and Fe(III)-bearing minerals. In homogeneous solutions with2.3 mM Fe(II), reduction of the nitrobenzenecompounds is thermodynamically favored; none-theless, after nearly 2 days, Klausen et al. (1995)did not observe appreciable reduction of the nitro-benzenes. Similarly, in heterogeneous solutions with-out aqueous Fe(II), but containing magnetite, amineral with structural Fe(II) and Fe(III), no appreci-able reduction of the nitrobenzenes occurred.

However, in heterogeneous solutions of aqueousFe(II) with magnetite, goethite or lepidocrocite (allFe(III)-bearing minerals), rapid reduction of the nitro-benzene compounds to anilines was observed. In addi-tion, the reduction reaction was found to be stronglypH-dependent, as is the sorption of Fe(II) on themineral surfaces. The nonlinear decrease of the rateconstant with increasing concentrations of the nitro-benzene compounds, together with the broad Fe(II)adsorption edge on these minerals, led Klausen et al.(1995) to suggest that multiple types of adsorbedFe(II) with differing reactivity participate in the nitro-benzene reduction reaction.

Reactions at mineral surfaces are also important indetermining the fate of inorganic contaminants, suchas uranium. Liger et al. (1999) studied the kinetics ofU(VI) reduction by Fe(II) in the presence or absenceof hematite (a mineral with structural Fe(III)). As fornitrobenzene reduction by Fe(II), no appreciable reac-tion was observed in homogeneous solutions contain-ing U(VI) and Fe(II) at pH 7.5 after 3 days, eventhough the reaction is thermodynamically favored.However, the addition of hematite to the U(VI)/Fe(II) solution led to reduction of UO2

12 withinhours (Fig. 12A). Liger et al. (1999) found thatthe rate constant for the reduction reaction variedboth with pH and with the total concentration ofFe(II).


C.

Ko

retsky

/Jo

urn

alo

fH

ydro

log

y2

30

(20

00

)1

27

–1

71

152Table 7Calculated and regressedCinner,TLM, protonation, deprotonation and electrolyte adsorption stability constants for the triple layer model from Sverjensky and Sahai (1996), Sahai andSverjensky (1997a,b), metal adsorption stability constants from Criscenti and Sverjensky (1999).Couter;TLM � 0:2 F/m2

Solid Site density (nm22) Electrolyte Cinner,CM (F m22) log K1a,log K2b

log KMc, log KLd, log K metal adsorption

Goethite 16.4e NaNO3 1.2 6.2,211.8 2.5, 2.0, 8.5f,g, 12.0f,h, 214.5i,j

NaCl 0.6 6.3,211.9 2.4, 2.4NaClO4 1.45 6.1,211.7 2.2, 1.7KNO3 1.1 6.2,211.8 2.3, 2.0LiNO3 1.4 6.2,211.8 2.3, 2.0

Corundum 30.5k NaNO3 1.2 6.1,211.8 2.5, 2.1, 8.1f,l


Ferrihydrite 11m NaNO3 1.2 6.6,212.2 2.5, 2.0, 2.4f,n


Gibbsite 6o NaNO3 1.2 7.0,212.7 2.2, 1.8NaCl 0.97 7.0,212.7 2.2, 1.8NaClO4 1.5 7.0,212.7 2.3, 1.8, 9.1n,l

KNO3 1.1 7.0,212.7 2.1, 1.8LiNO3 1.4 7.0,212.7 2.4, 1.8

Rutile 12.5e,k NaNO3 1.3 2.6,29.0 2.3, 2.4NaCl 0.97 2.6,29.0 2.4, 3.2NaClO4 1.45 2.7,29.1 2.5, 1.9KNO3 1.1 2.6,29.0 2.5, 2.2LiNO3 1.45 2.6,29.0 1.9, 2.2

Quartz 11.4e NaNO3 1.2 21.3,27.1 1.4, 1.2NaCl 1.0 21.3,27.1 0.9, 0.6,29.3i,p

NaClO4 1.5 21.3,27.1 1.4, 1.4KNO3 1.1 21.3,27.1 1.4, 1.2LiNO3 1.4 21.3,27.1 1.4, 1.2

C.

Ko

retsky

/Jo

urn

alo

fH

ydro

log

y2

30

(20

00

)1

27

–1

71

153

Table 7 (continued)

Solid Site density (nm22) Electrolyte Cinner,CM (F m22) log K1a,log K2b

log KMc, log KLd, log K metal adsorption

Silica 4.6q NaNO3 1.2 20.7,27.7 1.0, 0.9NaCl 0.98 20.7,27.7 0.7, 0.0,213.0g,i, 27.0g,r, 21.0g,s

NaClO4 1.5 20.7,27.7 0.9, 1.2KNO3 1.06 20.7,27.7 0.9, 0.9LiNO3 1.4 20.7,27.7 0.9, 0.9

Albite 11.5k NaNO3 1.2 1.6,28.8 2.0NaCl 0.97 1.6,28.8 2.0NaClO4 1.5 1.6,28.8 2.0KNO3 1.1 1.6,28.8 1.9LiNO3 1.4 1.6,28.8 2.1

a Stability constant for the protonation reaction:. SOH. H1�aq��. SOH1

2 :b Stability constant for the deprotonation reaction:. SOH�. SO21H1

�aq�:c Stability constant for electrolyte metal adsorption:. SO21M1

�aq��. SO2M1:

d Stability constant for electrolyte ligand adsorption:. SOH12 1L2

�aq��. SOH12 L2

:e Yates et al. (1977).f Stability constant for divalent metal adsorption:. SOH1 D12

�aq�1L2�aq��. SOHD12L2

:g Cd12.h Pb12.i Stability constant for divalent metal adsorption:. SOH1 D12

�aq�1H2O�. SO2DOH112H1�aq�:

j Ba12.k Koretsky et al. (1998).l Co12.

m Yates (1975).n Stability constant for divalent metal adsorption:. SOH1 D(aq)

12 1 L(aq)2 = . SOHDL1.

o McKinley et al. (1995).p Cu12.q Iler (1979).r Stability constant for divalent metal adsorption:. SOH1 D12

�aq��. SOD11H1:

s Stability constant for divalent metal adsorption:. SOH1 D12�aq��. SOHD12

:


Fig. 12. (A) Uranyl reduction kinetics by Fe(II) in homogeneous solution (circles), and in suspensions of hematite (squares).C is theconcentration of uranyl at timet; C0 is the initial concentration of uranyl. (B) Pseudo-first order reduction rate constant for U(VI) in thepresence of hematite as a function of the concentration of. FeIIIOFeIIOH calculated using a constant capacitance surface complexation model.After Liger et al. (1999).

To better understand the reaction mechanism, sothat the variation in the reduction rate constantmight be quantified, Liger et al. (1999) turned tosurface complexation modeling. Adsorption experi-ments using either aqueous U(VI) or Fe(II) withhematite were modeled using a constant capacitancesurface complexation model. The results suggested

that two Fe(II) surface complexes, [. FeIIIOFeII]1

and . FeIIIOFeIIOH and only one U(VI) surfacecomplex, . FeOUO2OH are present on hematiteover a pH range of approximately 5–9. From thesesurface complexation modeling results, a lineardependence of the apparent reduction rate constant(kobs) on the concentration of the. FeIIIOFeIIOH


Fig. 13. (A) Anorthite dissolution rates (in mol Si m22 s21) as a function of pH. Filled circles represent experimental data from Amrhein andSuarez (1988) measured at room temperature in NaCl at various ionic strengths using a batch reactor. (B) Microcline dissolution rates (inmol Si m22 s21) as a function of pH. Filled circles represent experimental data from Schweda (1990) measured at room temperature in HCl/LiOH at various ionic strengths using a flow-through reactor.

surface complex could be demonstrated (Fig. 12B),leading to the proposed reduction rate law,

d�U�VI ��dt

� 2k�. FeIII OFeII OH��U�VI ��ads: �19�

In other words, the two Fe(II) surface complexes onhematite are of differing reactivity, such that onlythe . FeIIIOFeIIOH species contributes significantlyto the reduction reaction. Liger et al. (1999) suggestedthat the pH dependence of nitrobenzene reductionrates observed by Klausen et al. (1995) might alsobe due to greater reactivity with the. FeIIIOFeIIOHspecies than with the [. FeIIIOFeII]1 species. Both ofthese experiments underscore the great importance ofcharacterizing the structure and reactivity (i.e.complexation) of surface species, in order to elucidatesurface reactions.

4.3.2. Mineral dissolution ratesBecause the chemical weathering of silicate miner-

als is of such importance in geochemical systems, ithas been studied by geochemists for well over acentury, in the field, in the laboratory and using theo-retical methods. As silicate minerals exposed at theearth’s surface weather, they contribute to the forma-tion of soils. In fact, the composition of ‘parent rock’is one of the primary factors in determining the type ofsoils to form and in controlling the long-term concen-trations of many plant nutrients in soil solutions (seetextbooks such as: Sparks, 1995; Brady and Weil,1996). In recent decades, acid rain has had a devastat-ing effect on soils both in Europe and America (e.g.Likens et al., 1996). In watersheds located in areaswhere crystalline rocks dominate, chemical weather-ing of silicate minerals is often the only source of soilbuffering to counteract the effects of acid rain (seereview by: Sverdrup and Warfvinge, 1995). Thus,there is a heightened interest in predicting the kineticsof silicate mineral weathering in acidified watersheds.There is also interest in quantifying the kinetics ofweathering because of the role silicate mineral disso-lution plays in the global CO2 cycle (Berner, 1995).

The dissolution rates of many silicate minerals,including olivines (Wogelius and Walther, 1991;Pokrovsky and Schott, 1999), chain silicates (Rimstidtand Dove, 1986; Casey et al., 1993; Brantley andChen, 1995; Zhang et al., 1996), sheet silicates(Carroll-Webb and Walther, 1988; Wieland and

Stumm, 1992; Nagy, 1995; Zysset and Schindler,1996; Ganor et al., 1999), quartz and silica (Doveand Elston, 1992; Dove, 1994, 1995; Dove and Nix,1997) and feldspars (Chou and Wollast, 1984, 1985;Blum and Lasaga, 1991; Blum and Stillings, 1995;Welch and Ullman, 1996; Stillings and Brantley,1995; Stillings et al., 1996) have been investigatedusing batch or flow-through reactor methods. Inthese experiments, far-from-equilibrium rates aretypically measured under well-stirred conditions, sothat the mineral remains highly undersaturated withrespect to the solution. These studies have shown thatsilicate dissolution rates have a strong dependence onpH and temperature (see reviews by Brantley andChen, 1995; Dove, 1995; Nagy, 1995; Blum andStillings, 1995; Fig. 13). The pH value at which thedissolution rate reaches a minimum depends on boththe structure and composition of the mineral, and ingeneral, is less than the pHZPCof the mineral (Brantleyand Chen, 1995).

The temperature dependence of silicate dissolutionrates can generally be described using an Arrheniusequation. Reported activation energies for silicatedissolution range from,22 to 150 kJ/mol (e.g.Nagy, 1995; Brantley and Chen, 1995). However, ithas been suggested that activation energies should becorrected for the negative enthalpy associated withproton adsorption or the positive enthalpy associatedwith hydroxyl adsorption, which may change themeasured activation energy by tens of kJ mol21

(Casey and Sposito, 1992). It has also been suggestedthat the reported variation in activation energies,particularly as a function of pH, may be due to experi-mental conditions that were not far-from-equilibrium(Cama et al., 1999).

There is also experimental evidence suggesting thatthe interaction of organic acids and solution cations oranions with mineral surfaces may enhance or inhibitsilicate dissolution rates. For example, solutioncations such as Li1, Na1 and K1 may enhancefeldspar dissolution rates at high pH (Sjoberg, 1989;Schweda, 1990), while Al13 has been shown to inhibitquartz dissolution at high pH (Oelkers et al., 1994). Atlow pH, cations such as Li1, Na1, Sr12 and NH4

1 havebeen shown to inhibit feldspar dissolution (Schweda,1990; Strandh et al., 1997). Similarly, alkali and alka-line earth cations enhance quartz dissolution rates atnear neutral pH conditions (Dove and Nix, 1997;


Strandh et al., 1997). Organic ligands mayenhance aluminosilicate dissolution rates (Welchand Ullman, 1993; Hajash, 1994; Welch andVandevivere, 1994; Vandevivere et al., 1994),have little effect on measured dissolution rates(Mast and Drever, 1987; Welch and Vandevivere,1994) or may inhibit dissolution (Welch andVandevivere, 1994). Microbes may also selec-tively enhance mineral dissolution by adhering tosurfaces and producing protons, organic acids orextracellular polymers (Hiebert and Bennett, 1992;McMahon et al., 1992; Vandevivere et al., 1994;Banfield et al., 1999; Brantley et al., 1999a,b).

According to transition state theory of chemicalreactions, dissolution rates should depend on thedegree of undersaturation of the dissolution reaction,that is, on the magnitude ofDGr (Aagaard and Helge-son, 1982; Lasaga, 1981, 1984, 1995). At very highdegrees of undersaturation, the dissolution rate isoften assumed to be essentially independent ofDGr,but as the reaction approaches equilibrium, therate is expected to be proportional to the chemicalaffinity. Laboratory studies of the dependence ofdissolution rate on chemical affinity for kaolinite(Nagy et al., 1991; Devidal et al., 1997) and foralkali feldspars (Gautier et al., 1994; Alekseyev etal., 1997) have confirmed that rates are propor-tional to the chemical affinity as equilibrium isapproached. However, dissolution rates may notbe independent of the saturation state, even inhighly undersaturated systems (Oelkers et al.,1994; Van Cappellen and Qiu, 1997b) and ratesmay exhibit highly nonlinear dependence onsaturation state (Burch et al., 1993).

Measured dissolution rates are strictly valid onlyfor a given temperature, pH, solution composition,and mineral sample. In addition, dissolution rateexperiments are time-consuming to perform,commonly taking weeks or even months to achievesteady-state in flow-through-type reactors. Thismeans that it would be extremely impractical tomeasure all possible combinations of minerals,temperatures and solution compositions that mightbe of interest in studying geochemical processes.Therefore, attempts have been made to combineexperimentally determined rates with surfacecomplexation theory, so that silicate dissolutionmechanisms might be elucidated and used to develop

predictive silicate dissolution rate laws (Fu¨rrer andStumm, 1986; Wieland et al., 1988).

Furrer and Stumm (1986) suggested that mineraldissolution occurs in three steps. First, a reactantsorbs to the mineral surface, weakening metal–oxygen (M–O) bonds. Next, the reacting surfacespecies breaks the M–O bond, detaching from thesurface. In the final step, the detached species istransported from the surface and into the bulksolution. If the dissolution reaction is transport-controlled, then it is the last of these three stepsthat proceeds most slowly, whereas if the reactionis surface-controlled, then it is the second stepthat is rate-determining. For surface-controlleddissolution reactions, Fu¨rrer and Stumm postulatedthat the rate of reaction should depend on theconcentration of surface species that weaken M–O bonds at the surface. Therefore, they proposed arate law of the form,

R� k�CSH�n 1 kL�CS

L�; �20�whereR is the dissolution rate,k the apparent ratecoefficient for proton-promoted dissolution,kL theapparent rate coefficient for ligand-promoteddissolution, CS

H the concentration of protonatedsurface species,CS

L the concentration of surfacesites with sorbed ligand andn the reaction order(an integer if only one dissolution mechanism isinvolved at the protonated surface site). They usedthis rate law successfully to model the dissolutionrates of BeO andg-Al 2O3. Far-from-equilibriumdissolution rates for minerals including feldspars(Amrhein and Suarez, 1988; Koretsky, 1997),kaolinite (Wieland and Stumm, 1992; Koretsky,1997), quartz (Brady and Walther, 1990; Doveand Elston, 1992) and tephroite (Casey et al.,1993) have been modeled as a function of pHand ionic strength using equations analogous toEq. (20).

5. Microscopic to macroscopic: application oflaboratory data and theoretical models to silicateweathering in the field

Reactions at the mineral–water interface are oftenstudied using laboratory- or microscopic-scale experi-ments, yet the questions that geochemists try to


answer based on such experiments frequently involveprocesses that occur over much larger scales, bothspatially and temporally. Geochemists using theoreti-cal or experimental methods hope to gain insights intothe mechanisms of processes that occur in ‘thefield’, and to use that information to predict theeffects of changes in temperature, pressure, solutioncompositions and other variables on the process inquestion. However, there are often problemsassociated with extrapolation of small-scale resultsto large-scale systems, particularly if mechanismschange with scale or when heterogeneity becomessignificant.

5.1. Estimation methods

Field-scale studies of chemical weathering havefrequently focused on the use of solute fluxes to calcu-late chemical weathering rates of silicate minerals(Paces, 1983; Velbel, 1985, 1989; Swoboda-Colbergand Drever, 1993; see also review by Drever andClow, 1995). In this method, concentrations of chemi-cal species entering a catchment area by dry deposi-tion and atmospheric precipitation are subtracted fromthe concentrations of such species leaving the catch-ment area, typically in the form of surface runoff. Thedifference in the concentrations of solutes enteringand leaving the area is then attributed to chemicalweathering, changes in biomass and changes in the‘exchangeable pool’ of chemical species (i.e. concen-trations of chemical species in soil solutions or boundto mineral or organic substrates in the soil). Althoughstraightforward in concept, this method can be diffi-cult to apply in practice because concentrations ofspecies deposited by dry deposition, changes inbiomass and changes in the exchangeable pool ofchemical species are often difficult to assess. In addi-tion, the time-scale over which measurements aremade may significantly affect results because thegeochemistry may be dominated by seasonal orannual cycles. Other errors in calculated rates mayresult from the calculated outflow of solutes, whichare commonly based on surface runoff measurementsalone, neglecting outflow by groundwater recharge,and which may be biased toward baseflow conditions.

Most studies of silicate weathering rates usingsolute fluxes have found much lower rates thanare measured in laboratory studies. For example,

Velbel (1985) suggested that oligoclase, almandineand biotite weathering rates in a forestedwatershed at the Coweeta Hydrologic Laboratory(Otto, North Carolina) were up to three orders of magni-tude slower than reported values from laboratorymeasurements. Similiarly, Paces (1983) estimatedoligoclase dissolution rates in the field to be approxi-mately two orders of magnitude slower than thosereported in laboratory experiments. Swoboda-Colbergand Drever (1993) also found slower rates of silicatedissolution in the field than in the laboratory, but onlyby a factor of 200–400. In that study, laboratorydissolution rates were determined using well-characterized soil material collected from thefield area.

Other methods have also been used to estimatemineral weathering rates in the field. For example,the mean maximum depth of etch pits and etch pitsize distributions have both been used to estimaterates of weathering (MacInnis and Brantley, 1993;Brantley and Chen, 1995). Like estimates based onsolute fluxes in catchments, dissolution rates of miner-als in soils based on the depth or distribution of etchpits are generally slower than laboratory measure-ments by between one and four orders of magnitude.Trends in residual mineral abundances, grain sizedistributions and mineral surface area for mineralsin soil chronosequences (i.e. sets of soils of differentages developed from similar parent rocks under simi-lar conditions) have been used by White et al. (1996)to estimate feldspar and hornblende weathering ratesin the Central Valley of California. They, too, foundthat field estimates of weathering rates were as muchas five orders of magnitude slower than thoseobserved in laboratory experiments.

5.2. Comparison of laboratory and field derivedweathering rates

A cursory inspection of field and laboratory esti-mates of silicate dissolution rates certainly seems toreveal large discrepancies between the two. It may betempting to conclude from this that estimates fromone or the other (or possibly both!) are wrong.However, careful consideration should first be givento the appropriateness of many of the comparisonsthat have been made between field and laboratorybased rate estimates and to the claims that a


discrepancy exists between these estimates. In fact, athorough understanding of dissolution mechanismscombined with an understanding of field-scale hydrol-ogy reveals important differences in laboratory andfield conditions; it also suggests which of thesedifferences is most likely to contribute significantlyto the apparent discrepancies between field andlaboratory based rate estimates (see also: Drever andClow, 1995; Sverdrup and Warfvinge, 1995). Thepotentially significant differences between field andlaboratory conditions include: (1) solution composi-tion and temperature; (2) solid composition and struc-ture; and (3) transport conditions.

Solution composition is clearly important in deter-mining silicate dissolution rates: only if a solution isundersaturated with respect to a given mineral willthat mineral dissolve at all. Ionic strength, pCO2,and the concentration and speciation of metal ionsand organic ligands in solution have all been shownto influence silicate dissolution rates. Organic ligandsmay promote dissolution through surface reactionsthat presumably weaken metal–oxygen bonds(Welch and Ullman, 1993; Hajash, 1994). Becausemany laboratory measurements of dissolution ratesare made in solutions with organic buffers (to inhibitformation of secondary precipitates), laboratory-derived dissolution rates may be enhanced relativeto rates from natural settings with much lower concen-trations of organics. At the same time, it has beenshown that certain metals, such as Al, that might bepresent in higher concentrations in field solutions thanin flow-through reactor solutions, may inhibit dissolu-tion (Oelkers et al., 1994; Gautier et al., 1994). Othercations have been shown to either inhibit or enhancedissolution rates, depending on the mineral and the pHconditions; the effect of such enhancement or inhibi-tion of rates on field as compared to laboratory rates isat present unclear. The application of moresophisticated surface complexation models to try toelucidate reaction mechanisms, particularly withrespect to the contribution of surface sites of differingstructure and reactivity, may clarify the effects ofvarious sorbates on mineral dissolution rates.Decreasing temperature may also decrease silicatedissolution rates. Thus, dissolution rates measured at258C must be corrected to reflect the lower tempera-tures prevalent in most near-surface geologic systems(e.g. Millot et al., 1999; White and Bullen, 1999).

Mineral composition and structure, as well as theformation of secondary precipitates, are also impor-tant factors to consider in assessing dissolution rateestimates. Solid surfaces have been shown to undergo‘aging’ effects that cause the surface of the solid tobecome less reactive over time without changes in thespecific surface area of the solid. Processes that mightcontribute to decreasing reactivity with time includesurface reconstruction, slow annealing processes ofreactive surface sites, and poisoning by adsorbates.Eggleston et al. (1989) found that initial dissolutionrates of aged mineral powders were slower than ratesmeasured for fresh samples, possibly due to slowrelaxation of microcracks formed during grinding.Studies of silica early diagenesis indicate that suchprocesses may continue to occur over geologic time-scales (Van Cappellen and Qiu, 1997a,b; Van Cappel-len and Dixit, 1998). The effects of aging on dissolu-tion rates are still poorly understood; more research isrequired before quantitative assessments of sucheffects can be made with much certainty. Anotherpossible problem with comparisons of field andlaboratory weathering rates arises from the formationof secondary minerals. Field rates are generallyderived from solute fluxes, so that dissolutionfollowed by immediate precipitation of clays andother secondary minerals is not considered. Incontrast, laboratory rates are usually measured forthe congruent dissolution of minerals to form onlydissolved solutes. Experimental artifacts might alsolead to apparent differences in laboratory and fieldrates. For example, Berner and Holdren (1979)suggested that freshly ground minerals undergo veryhigh initial rates of dissolution due to the formation ofultrafine particles during sample preparation, andpossibly due to the formation of a disordered layerat the surface.

Differences in temperature, mineral structure andsolution composition may contribute somewhat to‘discrepancies’ in field- and laboratory-derived sili-cate weathering rates. However, inappropriate com-parisons of systems with very different transportconditions is almost certainly the single most signifi-cant cause of apparent differences in field- and labora-tory-derived estimates of silicate weathering rates.Unlike in the well-stirred reactors typically used inlaboratory experiments to measure dissolution rates,regions of stagnant flow can and do occur in field


systems, and this leads to strong gradients in satura-tion state between the mineral surface and the bulkpore water solution composition (Fig. 14). Field-derived dissolution rates are generally comparedto experimentally determined far-from-equilibriumrates, yet field conditions may not be far-from-equili-brium, particularly at the solution–mineral interface(Hochella and Banfield, 1995). It has been demon-strated experimentally that dissolution rates decreasedramatically as equilibrium is approached (Aagaardand Helgeson, 1982; Nagy et al., 1991; Burch et al.,1993; Lasaga, 1995; Devidal et al., 1997; Fig. 15).Thus, laboratory rate determinations may be signifi-cantly higher than those occurring in natural settingsthat are closer to saturation. In regions of stagnantflow, the dissolution regime of the mineral maychange from surface-controlled to transport-con-trolled, meaning that the dissolution rate will thendepend on how quickly the dissolved solutes areremoved from the region of the surface, rather thanhow quickly reactions at the surface occur. In most

laboratory experiments, measurements are made underconditions of surface-controlled dissolution, such thatchanges in stirring rates (i.e. increased flow rates) donot change dissolution rates. However, some fieldweathering rates have been shown to depend onflow rates, suggesting that mineral dissolution atthese sites, unlike in many laboratory experiments,is transport-controlled (Schnoor, 1990; Fig. 16).

The second most likely source of error in estimatingsilicate weathering rates in the field is due to inaccu-rate determinations of the reactive surface area of thedissolving minerals. In laboratory experiments, thesurface area of the dissolving mineral is always incontact with solution, so the reactive surface areamay be easily calculated using, for example, BETmeasurements of the surface area of the dissolvingmaterial. In the field, however, reactive surface areadepends not only on the actual surface area of miner-als, but it also depends strongly on flow conditions,because all of the available surface area of minerals ina catchment will not always be wetted and undergoingdissolution, even if they are undersaturated withrespect to the bulk solution composition over thecatchment area. Recent attempts to calculate reactivesurface area by combining laboratory-derived silicateweathering rates with a 1D reaction–diffusion modelled to estimated reactive surface areas of the sameorder of magnitude as those determined by BET meth-ods (Steefel and Lichtner, 1998). This highlights theimportance of incorporating realistic descriptions oftransport into chemical weathering models.

5.3. Integration of field, laboratory and theoreticalstudies

To apply silicate dissolution rates derived fromlaboratory studies to field conditions requires asufficient understanding of both dissolution mechan-isms and field-scale hydrology, so that meaningfulcomparisons can be made. Theoretical models ofsurface-controlled mineral dissolution have helpedto elucidate the role that solution composition,mineral surface area, temperature and other variablesmight play in enhancing or inhibiting measureddissolution rates. Without such mechanistic modelsof silicate dissolution, it would be more difficult toresolve differences between rates measured underthe very different conditions generally used in


Fig. 14. Flow through a layer of porous media with zones of stagna-tion. Minerals that are within the zones of stagnated flow will becloser to equilibrium with respect to the aqueous phase than willminerals in the bulk of the layer. This is also depicted in a schematicdiagram of the saturation state through a cross-section (from A to B)of the layer. Solutions in the middle, where flow is highest, are moreundersaturated than minerals in the stagnant zones.

laboratory experiments as compared to field-scalesystems. At the same time, weathering models mustinclude more sophisticated descriptions of transportprocesses in the field. Far-from-equilibrium dissolu-tion rates derived in the laboratory cannot be directlycompared to field conditions where minerals incontact with solution are close to saturation, even ifthe bulk mineral composition in the field is under-saturated with respect to the average solution compo-sition in the field. With this in mind, ‘discrepancies’between field and laboratory dissolution rates can beexplained.

Velbel (1985) suggested that the three orders ofmagnitude difference between field and laboratorysilicate weathering rates found in his study of aNorth Carolina watershed was primarily due togeometrical estimates of total mineral surface areabased on average grain size, morphology and modal

abundance of minerals within the saprolitic zone ofthe watershed. Actual reactive surface area isprobably much less, due to inhomogeneous flowthrough pore or fracture networks in the saprolite.Non-reactive coatings on mineral grains might alsoconsiderably decrease the reactive surface area ofsilicates in the watershed (Velbel, 1989). In addition,Velbel did not account for the possibility that regionsof stagnant flow in the saprolitic zone might lead tolocal regions where minerals approach saturation withrespect to the percolating solution, creating decreasesin the local weathering rate.

Paces (1983) found field weathering rates to beapproximately two orders of magnitude slower thanthose derived from far-from-equilibrium mineraldissolution studies. He attributed the lower fieldweathering rates primarily to differences in thesurface characteristics of aged feldspars present in


Fig. 15. Kaolinite dissolution rates at 808C and pH, 3 as a function ofDG=RT: Positive rates indicate mineral growth; negative rates indicatemineral dissolution. Positive values ofDG=RT indicate supersaturation; negative values ofDG=RT indicate undersaturation. After Nagy et al.(1991).

the field, compared to fresh feldspar surfaces usedin laboratory studies. However, as in the study ofVelbel (1985), the lower field rate estimates mayarise partially from problems in estimating reactivesurface area. Paces equated estimates of fracture andpore surface area in the field to the total reactivesurface area. However, if only a fraction of thefractures or pores actively conducted flow, theestimated reactive surface area in the field wouldbe too high, leading to rates lower than those observedin well-stirred laboratory reactors. Also, as in thestudy of Velbel (1989) the possibility of regionsof stagnant flow, where minerals might approachsaturation with respect to the solution, was not consid-ered. This could also result in lower field weatheringrates.

Research efforts need to be directed at combiningsophisticated field-scale geochemical models ofmineral water interactions with sophisticated hydro-

logical models. At present, detailed models ofgeochemical reactions are typically combined withextremely simplified treatments of hydrological para-meters. For example, Paces (1994) has developed amodel to describe the hydrologic and biogeochemicalresponse of a catchment area to anthropogenic inputs.In this model, homogeneous speciation, equilibriumadsorption, heterogeneous equilibrium (precipita-tion–dissolution reactions), mineral dissolutionkinetics, and the variation of rate and equilibriumconstants are all described. However, the hydrologyof the system is represented very simply, as a series ofwell-mixed reservoirs. At the same time, advancedhydrologic models are frequently combined withvery simple representations of geochemical reactions,for example, using distribution coefficients to modeladsorption (see discussion in Tompson and Jackson,1996).

Combining geochemical models based on


Fig. 16. Log of dissolved silica release rates (representing net chemical weathering rates) as a function of log of flow rate normalized to the massof soil. Rates are from field measurements (filled circles) and laboratory (open circle) experiments. At high flow rates, the release rate of silicadoes not depend on the flow rate, suggesting that dissolution is surface-controlled. However, at low flow rates, the log of the silica release rate isproportional to the log of the flow rate normalized to the mass of soil, suggesting that dissolution rates at these sites are transport-limited. AfterSchnoor (1990).

microscopic-scales with hydrologic models at thefield-scale may also be difficult because the hetero-geneity of the field-scale system must be con-sidered (Behra, 1994). Although this may bedifficult to represent using strictly deterministicmodels, combining stochastic models of mineraldissolution with stochastic representations of thechemical and physical structure of field-scale systemsmight yield more realistic models of mineral waterreactions in the natural environment. There existsgreat potential for enhancing our current understand-ing of coupled field-scale geochemical and hydrologicprocesses by developing models that represent boththe hydrology and the geochemistry as realisticallyas possible.

6. Conclusions

Water–rock interactions affect geologicprocesses ranging from chemical weathering tothe degradation and mobility of hazardous chemi-cal species to nutrient availability in soils to theformation of ore deposits. These interactionsbetween aqueous solutions and mineral surfacesdepend on characteristics of both the chemicalspecies in solution and also on the complex andhighly varied structure and composition of mineralsurfaces. New microscopic, spectroscopic andtheoretical methods are rapidly being developedand applied to characterization of mineralsurfaces. With improved data regarding mineralsurface topography and composition, more sophis-ticated models of reactions at the mineral–waterinterface can be developed.

Currently, a number of empirical models ofsurface adsorption are in wide use, as well as varioussurface complexation models that are based onthermodynamic principles. Empirical models includedistribution coefficient, ion exchange, Langmuir andFreundlich isotherm models of adsorption. Suchmodels must be calibrated in the laboratory beforebeing applied to a system of interest; they cannotbe readily extrapolated beyond strict experimentalconditions (temperature, pressure, pH, ionic strength,oxidation–reduction state, electrolyte composition),hence they may be tricky to apply to field-scalesystems. Surface complexation models, which are

very much analogous to aqueous speciation models,represent a significant improvement over strictlyempirical models because calculations are validover wide ranges of solution composition. Thisis true because surface complexation modelsaccount explicitly for changes in surface electricalproperties and in structures of adsorbed species,which determines their reactivity, as a function ofsolution composition. Although widespread applica-tion of surface complexation models has beenhampered by a lack of available thermodynamic para-meters, internally consistent databases are beingdeveloped to describe pure solids, and attempts arebeing made to measure or predict parameters fornatural systems.

Mineral surfaces are often studied at a microscopicscale, and this atomic- or near-atomic-scale informa-tion is used, together with bulk solution (laboratory-scale) evidence, to develop models of reactions at themineral–water interface. However, many questionsthat might be addressed using such models concernsystems of much larger scale. For example, there is agreat deal of interest in characterizing chemicalweathering rates of silicate minerals, which havebeen shown to play a significant role in bufferingacidified watersheds and in determining the long-term availability of nutrients and toxins to plantsand other soil organisms. Although it has beenclaimed that chemical weathering rates from fieldand laboratory data disagree by as much as four ordersof magnitude, the apparent discrepancy can beexplained by taking into account the inherent differ-ences in laboratory and field conditions, especiallydifferences in saturation state and reactive sur-face area. Improved mechanistic interpretations ofchemical weathering rates will help to refine modelsof both laboratory- and field-scale weathering reac-tions by allowing more accurate accounting of theeffects of temperature, pH, solution composition,surface area and saturation state on rates, butequally importantly, improved representation offield hydrology must be included in weatheringmodels. Linking sophisticated hydrologic modelsto sophisticated geochemical models offers greatpotential in furthering our understanding of processesas diverse as contaminant degradation, nutrientcycling in soils, ore deposit formation, and chemicalweathering.


Acknowledgements

This paper was much improved by conversationswith Johnson Haas, Kimberley Hunter, and ChristofMeile. Comments on an early version of the manu-script from Craig Allen, Louise Criscenti and PhilippeVan Cappellen are greatly appreciated. Thoroughreviews of the manuscript by C. Steefel and P. Bennetwere of great benefit and are much appreciated. Finan-cial support was granted by US Environmental Protec-tion Agency (R-825397) and Office of Naval Research(N00014-98-1-0203).

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