Research On Points of Zero Charge GARRISON SPOSITO* Ecosystem Sciences Division, Hilgard Hall 3110, University of California, Berkeley, California 94720-3110
Following on the pioneering efforts of Werner Stumm and his collaborators, environmental chemists have developed increasingly detailed molecular models of the adsorbentaqueous solution interface in order to quantify the pH dependence of surface charge. This model development, irrespective of its level of sophistication, is subject to a few broad constraints, which may be termed generic properties of surface charge, that in turn reflect certain macroscopic conditions imposed by electroneutrality and thermodynamic stability. In this paper, rigorous proofs of these generic properties are given, and the results are used to establish general connections among conventional points of zero charge that all molecular models of the electrical double layer must respect. The nonunique relationship between a molecular model of the electrical double layer and the observed effects of ion adsorption on points of zero charge is emphasized.
Introduction The concept of the point of zero charge was born with the present century in studies of the flocculation of hydrophobic colloids (ref 1, p 80). Almost immediately as the importance of pH was recognized for the behavior of colloidal systems, controversy erupted as to the chemical significance of solution proton activity in the presence of charged adsorbents and even as to whether pH could be measured objectively in a suspension of natural particles (2). These historical travails, often laced with nationalism, finally were resolved (2, 3) in favor of “master variable” status for pH in the aqueous surface chemistry of charged particles. In the first of a remarkable series of papers published in Croatica Chemica Acta, Stumm et al. (4) invoked a point of zero charge in providing a reference state from which to express the acid-base reactions of hydroxyl groups on the surfaces of oxide minerals. Using straightforward massaction descriptions of these surface reactions, they demonstrated that the proton concentration in aqueous solution at the “zero point of charge” [now termed the point of zero net proton charge, pznpc (5)] was equal to the geometric mean of two acid-base equilibrium constants. In the second paper of the series (6), the zero point of charge was compared with the pH value at which a colloidal particle is “electrokinetically uncharged” [the isoelectric point, iep (7)]. Stumm et al. (6) argued persuasively that strong metal cation adsorption on an amphoteric colloid suspended in an electrolyte solution would lower its zero point of charge but would raise its isoelectric point. This interesting observation was embellished with the statement that these two points of zero charge could be equal only if strong adsorption of electrolyte ions by a charged colloid did not occur. * Corresponding author telephone: (510)643-8297; fax: (510)6432940; e-mail:
[email protected]. S0013-936X(98)00234-X CCC: $15.00 Published on Web 08/14/1998
1998 American Chemical Society
Nearly 30 years after the pioneering work of Stumm et al. (4, 6), the prediction of the points of zero charge of amphoteric adsorbents through chemical models of the particle-water interface has become a flourishing industry in aqueous environmental chemistry (8-11). The most recently invented models are evolving toward a truly molecular picture of the Bronsted acidity of natural particle surfaces, with a predictive value that emerges in consonance with structure-reactivity relationships. It is therefore especially useful at this juncture to have firmly in hand an intellectual grasp of the points of zero charge that transcends all attempts at molecular model building; i.e., to understand the generic properties of these pH values that any molecular model of them must respect. The generic properties refer to behavior that derives solely from the existence of conservation laws and from the conditions of chemical stability, irrespective of any molecular mechanism of adsorption. The present paper is an attempt to describe these properties based on the concept of surface charge balance (12) and on the use of thermodynamic stability conditions that are relevant to proton adsorption reactions. The objective of this paper, which corrects and improves on three earlier studies (5, 12, 13), is to delineate the purely macroscopic properties of the points of zero charge that cannot be used by any molecular model of the particlewater interface to claim uniqueness but which can serve always to disabuse any model that cannot reproduce them.
Surface Charge Balance Operational Categories of Surface Charge. Natural particles develop surface charge from structural substitutions and disorder (including defects) and from reactions they undergo with ionic species in aqueous solution (ref 14, p 43). The surface charge developed by these mechanisms is classified conventionally into three operational categories, each of which also carries the modifier “specific” if measured in molc kg-1 (15): (i) structural, denoted by σo; (ii) adsorbed proton, denoted by σH; and (iii) adsorbed ion, dentoed by q+ - q≡ ∆q, where q is the total relative adsorption (7) of cation (+) or anion (-) charge, i.e., a sum over the relative adsorption multiplied by the absolute value of the valence for each adsorbate ion (5). Conventionally, ∆q includes contributions from all possible modes of ion adsorption but excludes H+ and OH- bound in surface complexes because these species are, by definition, the sole contributors to σH (ref 14, p 47). This partitioning of adsorbed protons and hydroxide ions into two different categories of surface charge honors the traditional importance of H and OH as components of hydroxylated adsorbents (16). The categories of surface charge are connected closely to conventional methods of measurement (17): (i) Cs+ adsorption for σo as related to the clay minerals; (ii) potentiometric titration for σH; and (iii) the Schofield method of index ion adsorption for ∆q. Although these laboratory methods can be applied to highly heterogeneous samples of soils or sediments that contain crystalline minerals, poorly ordered solid adsorbents, and biota, their chemical specificity in quantifying surface charge depends on the extent to which unwanted side reactions (e.g., adsorbent dissolution, aqueous complex formation) can be suppressed or taken into account by calibration. Careful discussions of the side-reaction issue have been given by Huang (18), Charlet et al. (19), and Zelazny et al. (17). Charge Balance. Measured values of σo, σH, and ∆q are subject to the constraint of surface charge balance (12): VOL. 32, NO. 19, 1998 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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σo + σH + ∆q ) 0
(1)
Equation 1 attests to the necessary overall electroneutrality of any sample of natural particles that has been equilibrated with an aqueous electrolyte solution. Structural charge and particle charge attributable to surface-complexed protons and hydroxide ions must be balanced with the net surface charge that is contributed by all other adsorbed ions (and by H+ or OH- adsorbed in the diffuse ion swarm). Equation 1 can be (and should be) used to test experimental surface charge data for self-consistency. A convenient approach is to plot ∆q against σH over a range of pH values for which these two surface charge components have been measured (20). A simple rearrangement of eq 1
∆q ) -σH - σo
(2)
shows that the slope of this “Chorover plot” must be equal to -1, with both its y- and x-intercepts equal to -σo. Figure 1 illustrates the application of eq 2 to a kaolinitic oxisol (a highly weathered tropical soil comprising kaolinite, metal oxides, and quartz as well as organic matter) that was equilibrated with LiCl solution at three different ionic strengths over the pH range 2-6 (20). The line through the data is based on the regression equation
∆q ) -1.01 ( 0.07σH + 12.5 ( 0.8
r 2 ) 0.92*** (3)
with both ∆q and σH expressed in units of mmolc kg-1 and 95% confidence intervals following the values of the slope and intercept. The value of σo independently measured was -12.5 ( 0.04 mmolc kg-1, in excellent agreement with the yand x-intercepts in eq 3. Chorover plots also have been used recently to test surface charge data for specimen kaolinite (21) and for temperate-zone soils with mixed clay mineralogy and organic matter (22). This kind of consistency examination necessarily should precede any interpretation of experimental surface charge data in terms of a chemical model of the solid-aqueous solution interface. Auxiliary Categories of Surface Charge. Applications of eq 1 to the surface reactions of natural adsorbents are facilitated by some nominal rearrangements among the categories of surface charge. The first two terms on the left side of eq 1 can be grouped together to define the intrinsic charge, σin (5):
σin ≡ σo + σH
(4)
which is intended to represent components of surface charge developed from the adsorbent structure. The third term on the left side of eq 1 can be decomposed in molecular terms into three subcategories (12):
∆q ≡ σIS + σOS + σd
(5)
which refer, respectively, to the net charge of ions adsorbed in inner-sphere surface complexes (IS), in outer-sphere surface complexes (OS), or in the diffuse ion swarm (d). The utility of eq 5 depends on the extent to which experimental detection and quantitation of surface species is possible. Experimental detection requires a spectroscopic approach. Prototypical examples of surface complexes involving environmentally important metal cations adsorbed on hydroxylated particle surfaces recently have come from the XAFS studies of the Manceau group (23, 24) and of the Brown group (25, 26). These kinds of careful spectroscopic investigations are necessary precursors to all methodologies that purport to quantitate surface complexes formed in ion adsorption reactions. 2816
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FIGURE 1. Chorover plot of surface charge data for a kaolinitic tropical soil suspended in LiCl solutions of varying ionic strength (open circles: 0.001 mol kg-1; crosses: 0.005 mol kg-1; filled circles: 0.010 mol kg-1). The data are from Chorover and Sposito (20). Partitioning of surface complexes into inner-sphere and outer-sphere types is not always possible (or required) however, and eq 5 can alternatively be written in the simpler form:
∆q ≡ σS + σd
(6)
where σS denotes the Stern layer surface charge (7) representing all adsorbed ions not in the diffuse ion swarm. This latter conceptual distinction, based largely on adsorbed ion mobility, is epitomized by defining the total particle charge, σp (5, 14):
σp ≡ σin + σS
(7)
which is the net surface charge contributed by the adsorbent structure and by adsorbed ions that are immobilized in surface complexes (i.e., adsorbed ions that do not engage in translational motions relative to the adsorbent that may be likened to the diffusive motions of a free ion in aqueous solution).
Points of Zero Charge Definitions. Points of zero charge have been defined traditionally as pH values for which one of the categories of surface charge is equal to zero, at some ambient temperature, applied pressure, and aqueous solution composition (5, 7, 14). Other master variables than pH (e.g., the negative logarithm of the aqueous solution activity of any ion that adsorbs primarily through inner-sphere surface complexation) can be utilized to define a point of zero charge (27, 28), but pH will remain the exemplary variable in the present paper. Three standard definitions are listed in Table 1 (5, 14, 17). The pznpc is the pH value at which the net proton surface charge is equal to zero (5, 14). Perhaps the most straightforward (if seldom used) method to determine this pH value would be to measure ∆q as a function of pH and then locate the pH value at which ∆q ) -σo, thus taking direct advantage of eq 1 (21, 29), given that a separate measurement of σo has been made. Despite ample good advice to the contrary, (28, 30), most published reports of pznpc values based on the common use of potentiometric measurements to determine
TABLE 1. Conventional Points of Zero Charge IUPAC symbola
name
definition
pznpc pznc pzc
point of zero net proton charge point of zero net charge point of zero charge
σH ) 0 σin ) 0 σp ) 0
a IUPAC nomenclature (15) requires periods to follow each letter in the symbol (e.g., p.z.c.).
σH do not respond to the fact that these titrations yield only changes in σH relative to the net proton surface charge at the beginning of a titration experiment. An additional independent measurement always is needed to establish the true value of σH (19-21, 29, 31). Unfortunately, this renormalization of the titration σH cannot be done unambiguously by the common device of choosing σH ≡ 0 at the crossover point of two (or more) apparent σH versus pH curves that have been determined at different ionic strengths (28, 30). Indeed, each such apparent σH curve is, in principle, offset from a true σH curve by a different (as-yet unknown) amount that corresponds to the particular initial state of the titrated system, thus making even the crossover point illusory. For the most part, the necessary additional experimental work has not been done, leaving the published surface geochemistry database littered with spurious pznpc values. The pznc is the pH value at which the intrinsic surface charge is equal to zero (5). Comparison of eqs 1 and 4 shows that surface charge balance requires the condition
σin + ∆q ) 0
(8)
i.e., the net adsorbed ion charge vanishes at the pznc. Common practice is to utilize index ions such as K+ and Clin the determination of pznc from a ∆q versus pH curve (17). Evidently, the value of pznc will depend on the choice of index ions, although experience shows that this dependence is often small if these ions are chosen from the following group: Li+, Na+, K+, ClO4-, and NO-3 (17). Methods of measuring pznc for soils and sediments have been reviewed by Zelazny et al. (17), who also provide tabulations of representative values for specimen minerals. As a broad rule, pznc values for silica, humus, clay minerals, and most manganese oxides or oxyhydroxides are below pH 4, whereas those for aluminum and iron oxides or oxyhydroxides and for calcite are above pH 7. Thus, the pznc will tend to increase as the extent of geochemical weathering of a soil or sediment increases (32). The pzc is the pH value at which the net total particle charge is equal to zero (5, 14). Thus, by eqs 1 and 4-7, at the pzc there is no surface charge to be neutralized by ions in the diffuse swarm, and any adsorbed ions that exist must be bound in surface complexes. Therefore, the pzc can be measured by ascertaining the pH value at which a perfect charge balance exists among the ions in an aqueous solution with which particles have been equilibrated (14, 19). Charlet et al. (19), following an approach outlined by Stumm (14), have determined the pzc this way by speciating an aqueous solution phase equilibrated with a solid adsorbent before titration and then invoking the constraint of overall electroneutrality (proton condition) on the aqueous species charge concentrations. More commonly, pzc is inferred from the pH value at which a suspension flocculates rapidly (27) or from that at which the particle electrophoretic mobility vanishes, the iep (7). Equality between iep and pzc however is problematic because it requires demonstrating experimentally that no part of the diffuse ion swarm will be advected with a particle as it moves steadily in response to a uniform, constant electric field. Otherwise, the iep must correspond to the vanishing of σp plus some poorly defined fraction of
the diffuse swarm charge. Fair and Anderson (33) have added complexity to this issue in a model calculation of the electrophoretic mobility for ellipsoidal particles that carry zero net total charge but have a heterogeneous surface charge distribution (i.e., zero net particle charge because of mutually cancelling patches of positive and negative surface charge). These model particles, whose shape can range from prolate to oblate, not unlike those found in natural soils, also were assumed to have a “no-slip” boundary condition at the solidliquid interface, thus obviating the problem of diffuse swarm advection. With any distribution of surface charge that yields a nonzero electric quadrupole moment for these neutral particles, there also will be a nonzero electrophoretic mobility despite the existence of zero net surface charge overall. Fair and Anderson (34) illustrate this conclusion for an ellipsoid of revolution that has a band of positive charge sandwiched between two canceling bands of negative charge distributed along the ellipsoid symmetry axis. If its shape is either prolate or oblate, this electrically neutral particle will have a nonzero electrophoretic mobility. Thus σp ) 0 is not sufficient to imply that the iep has been achieved for these nonspherical, charge-heterogeneous particles. Stability Conditions. Equation 1 implicitly imposes a constraint on changes in the net proton charge and/or net adsorbed ion charge that may occur in response to imposed changes in adsorbate or adsorptive composition at fixed temperature (T) and applied pressure (P):
δσH + δ∆q ) 0
(9)
where δ represents an infinitesimal shift caused by any mechanism that does not alter the adsorbent bulk structure or composition (i.e., σo is to remain constant during any process causing the shift δ). For example, if the ionic strength (I) of the aqueous solution equilibrated with a solid adsorbent is changed at fixed T and P, eq 9 takes the form
( ) ( ) ∂σH ∂I
∂∆q ∂I
+
T,P
T,P
)0
(10)
This constraint equation may be applied to the definition of the point of zero salt effect (pzse; 5, 14, 17)
( ) ∂σH ∂I
T,P
)0
(pH ) pzse)
(11)
to show that the crossover point of two σH versus pH curves must also be that of two ∆q versus pH curves (31), a fact that can be used to check illusory pzse values inferred from the crossover point of titration σH instead of true σH curves. Charge balance is not the only condition that must be preserved when changes are imposed on an adsorbentaqueous solution system in some quiescent state at fixed T and P. For changes between equilibrium states, any shift from one to the other must not alter the fact that the Gibbs energy of the system remains at a relative minimum value (34). This requirement yields the stability condition (35):
( ) ∂µi ∂ni
>0
(12)
T,P
where µi is the chemical potential of a component i whose mole number is ni. For the case of an equilibrated adsorbate, n can be replaced with the relative adsorption Γi(w) (7), and µi can be equated to the chemical potential of the adsorptive in aqueous solution (34):
µi ) µi0 + RT ln (i)
(13)
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adsorptive with which the adsorbate has come into equilibrium, R is the gas constant, and (i) is the activity of the adsorptive in the aqueous solution contacting the adsorbent. It follows from eqs 12 and 13 that thermodynamic stability imposes the following constraint:
( ) ∂ ln (i) ∂Γi(w)
>0
(14)
T,P
Equation 14 requires increases in the amount of an adsorbate to follow increases in the aqueous solution activity of the adsorptive with which it is equilibrated. An important application of eq 14 (after inversion) is to the response of specific net proton surface charge (5, 14)
σH ) ΓH(w) - ΓOH(w)
(15)
to changes in pH:
( ) ∂σH ∂pH
T,P
pznpc, σH must have a negative sign in eq 17 because of the condition on σH in eq 16 and the fact that σH ≡ 0 at pznpc (Table 1). It follows that σo > 0 if pznc > pznpc. Similarly, if pznc < pznpc, σo < 0. Therefore: The sign of the difference (pznc - pznpc), is also the sign of the structural charge σo. For example, Schroth and Sposito (21) found pznc ) 3.6 whereas pznpc ) 5.0 for a sample of Georgia kaolinite (KGa1). This result is an immediate clue that negative structural charge exists in some form in their sample [likely in a 2:1 clay mineral impurity (36)]. More generally, natural particles whose surface chemistry is dominated by 2:1 clay minerals (σo < 0) must always have pznc values below their pznpc values. An important corollary of the theorem above is that natural particles without 2:1 clay minerals [and, strictly speaking, without oxide or oxyhydroxide minerals having structural charge (37)] always have pznc ) pznpc. Equality of the two points of zero charge means that the pH value at which the true σH is equal to zero can be determined through ion adsorption measurements (31), quite independent of any titration experiment performed to measure the changes in σH relative to a pretitration state. An important chemical difference between pznc and the pzc is that a diffuse swarm can exist at the former pH value, whereas it cannot at the latter pH value (cf. eqs 5 and 7). The use of suspension flocculation to infer pzc (27, 28) is compromised by the fact that flocculation usually occurs in the presence of a small, but nonzero, diffuse ion swarm whose accompanying electrostatic repulsive force is simply too weak to preclude van der Waals attraction from inducing flocculation (28). The use of electrokinetic methods to infer pzc is problematic, as described above, because there may be no unique relationship between electrokinetic motion and surface charge for heterogeneous nonspherical particles (33). Surface charge balance, as expressed by combining eqs 1, 4, and 6 2818
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σin + σS + σd ) 0
(18)
may offer a way out of this operational dilemma. Suppose that σS ) 0 at the pznc. Then σd also must vanish because of eq 18 and the fact that σin ) 0 at the pznc (Table 1). But σd ) 0 means pH ) pzc. Therefore, pzc ) pznc if σS ) 0 at the pznc. Conversely, if pzc ) pznc, then σin ) 0 ) σd and, by eq 18, σS ) 0 of necessity. The general conclusion to be drawn is in the theorem: The pzc and pznc will be equal if and only if the Stern layer charge is zero at the pznc. As a corollary, pzc ) pznc trivially if the only adsorbed ion species are those in the diffuse swarm. Otherwise, ions adsorbed in surface complexes (other than H+ or OH-) must among themselves meet exactly the condition of charge balance at the pznc. This situation might occur for monovalent ions adsorbed in outer-sphere surface complexes by largely electrostatic interactions. Electrolytes for which σS ) 0 at the pznc may thus with justification be termed “indifferent electrolytes”, in the sense that relatively weak electrostatic interactions dominate their adsorption reactions. Natural particles contacting solutions of indifferent electrolytes should bear zero net total particle charge at the pznc. When measured in the presence of an (operationally defined) indifferent electrolyte, the pznpc often has had the modifier “pristine” added as an indicator of the absence of strongly adsorbing ions (30, 38). This terminology was introduced by Pyman et al. (38), who invoked a chemical model of ion adsorption (39) to illustrate the problematic effects of sulfate ions (assumed strongly adsorbing) on the crossover point of σH versus pH curves determined in the presence of varying concentrations of nitrate ions (assumed indifferent). Lyklema (30) developed this conceptualization further, corroborating the inconclusive behavior of crossover points, while noting with Stumm et al. (6) that the pznpc is shifted downward by a strongly adsorbing cation and upward by a strongly adsorbing anion, relative to its pristine value. These effects are commonly reported in the surface chemistry literature (6, 38, 40-42), usually in the context of some favorite chemical model of strong ion adsorption. That the observation of shifts in the pznpc is not straightforward to interpret chemically can be appreciated by considering the charge balance constraint in eq 9 applied at the pznpc. If the net adsorbed ion charge is made to increase, σH must correspondingly become negative, implying that the incipient pH value no longer is equal to the pznpc but instead must be higher than that (eq 16). Thus, an increase in ∆q leads to a decrease in the pznpc. By the same line of reasoning, a decrease in ∆q leads to an increase in the pznpc. One concludes, therefore: If the net adsorbed ion charge increases, the pznpc decreases and vice versa. The broad implication of this result is that additional cation adsorption by any mechanism tends to decrease the pznpc, and additional anion adsorption by any mechanism tends to increase the pznpc. There is accordingly no necessary relationship between strong ion adsorption and shifts in the pznpc, since a mere change in the relative population of the diffuse ion swarm would be sufficient to change the pznpc as a direct result of surface charge balance (eq 9) and the stability condition in eq 16. Chemical models that predicate shifts in the pznpc solely on strong ion adsorption function simply as special premises of the theorem above (i.e., they display sufficiency, not necessity). The behavior of the pznpc under changes in ion adsorption may be contrasted with that of the pzc. If pH ) pzc, the diffuse swarm is not present and eq 9 becomes (cf. eq 6):
δσH + δσS ) 0
(pH ) pzc)
(19)
If the Stern layer charge is made to increase, then the net proton charge must compensate this change by decreasing,
which, according to eq 16, requires the pzc also to increase. In other words, the pH value at which σH + σS just balances σo must be higher as σS becomes higher in order that σH will be negative enough (eq 16) to contribute its full measure to charge balance. In the same way, the pH value at which σd ) 0 must be lower as σS becomes lower in order that σH will become positive enough to compensate exactly the decrease in σS. It follows that: If the Stern layer charge decreases, the pzc also decreases and vice versa. This theorem indicates the key role of cation surface complexation in increasing pzc and that of anion surface complexation in decreasing pzc. It does not imply, however, that shifts in pzc necessarily signal the effects of strong ion adsorption, since a change in the number of outer-sphere surface complexes alone is sufficient. Overall, one concludes that no unambiguous information about strong ion adsorption can be obtained from shifts in pznpc or in pzc as a result of changing ion adsorption characteristics. These generic properties of the points of zero charge illustrate the essential ambiguity of macroscopic chemical measurements when faced with the issue of adducing molecular mechanisms. The lack of uniqueness among points of zero charge as signatures of underlying molecular behavior is perhaps most poignantly expressed in eq 10, which provides for the only rigorous macroscopic connection between pzse and a true point of zero charge. If ∆q and its first derivative with respect to ionic strength both vanish at the same pH value, then pzse ) pznc. Little more can be said without invoking some detailed concept of interactions in the electrical double layer, and no detailed conceptualization is likely to show that the pzse has fundamental surface chemical significance (30, 38). More generally, matters could not be summarized better than the wise counsel given by Stumm et al. (42) in the third article of the Croatica Chemica Acta series: Thus, all the models may be viewed as being of the correct mathematical forms to represent the data but are not necessarily an accurate physical description at the interface. In other words, all models can be used to describe experimental data over the range of experimental data; the “intelligence” of the data, on the other hand, is not sufficient to gain insight into the physical nature of the interface.
Acknowledgments The research reported in this paper was supported in part by NSF Grant EAR-9505629. Thanks to Jon Chorover for providing Figure 1; to Paul Schindler, Sephan Kraemer, and Sing-foong Cheah for reviewing this paper while in draft form; and to Angela Zabel for excellent preparation of the typescript.
Literature Cited (1) Kruyt, H. R. Colloid Science, Vol. 1, Irreversible Systems; Elsevier: Amsterdam, 1952. (2) Bolt, G. H. Adv. Geoecol. 1997, 29, 177-210. (3) (a) Babcock, K. L.; Overstreet, R. Science 1953, 117, 686-687. (b) Overbeek, J. Th. G. J. Colloid Sci. 1953, 8, 593-605. (4) Stumm, W.; Huang, C. P.; Jenkins, S. R. Croat. Chem. Acta 1970, 42, 223-245. (5) Sposito, G. In Environmental Particles, Vol. 1; Buffle, J., van Leeuwen, H. P., Eds.; Lewis Publishers: Boca Raton, FL, 1992; pp 291-314. (6) Stumm, W.; Hohl, H.; Dalang, F. Croat. Chem. Acta 1976, 48, 491-504. (7) Everett, D. H. Pure Appl. Chem. 1972, 31, 578-638.
(8) Sverjensky, D. A. Geochim. Cosmochim. Acta 1994, 58, 31233129. (9) Felmy, A. R.; Rustad, J. R. Geochim. Cosmochim. Acta 1998, 62, 25-31. (10) (a) Sverjensky, D. A.; Sahai, N. Geochim. Cosmochim. Acta 1996, 60, 3773-3797. (b) Hiemstra, T.; van Riemsdijk, W. H. J. Colloid Interface Sci. 1996, 179, 488-508. (11) Goldberg, S. In Structure and Surface Reactions of Soil Particles; Huang, P. M., Senesi, N., Buffle, J., Eds.; Wiley: London, 1998; pp 377-412. (12) Sposito, G. Soil Sci. Soc. Am. J. 1981, 45, 292-297. (13) Sposito, G. Chimia 1989, 43, 169-176. (14) Stumm, W. Chemistry of the Solid-Water Interface; Wiley: New York, 1992. (15) Mills, I.; Cvitas, T.; Homann, K.; Kallay, N.; Kuchitsu, K. Quantities, Units and Symbols in Physical Chemistry, 2nd ed.; Blackwell Scientific: Oxford, 1993. (16) Schindler, P. W.; Stumm, W. In Aquatic Surface Chemistry; Stumm, W., Ed.; Wiley-Interscience: New York, 1987; pp 83110. (17) Zelazny, L. W.; He, L.; Vanwormhoudt, A. In Methods of Soil Analysis, Part 3sChemical Methods; Sparks, D. L., Ed.; Soil Science Society of America: Madison, WI, 1996; pp 1231-1253. (18) Huang, C. P. In Adsorption of Inorganics at Solid-Liquid Interfaces; Anderson, M. A., Rubin, A. J., Eds.; Ann Arbor Science: Ann Arbor, MI, 1981; pp 183-217. (19) Charlet, L.; Wersin, P.; Stumm, W. Geochim. Cosmochim. Acta 1990, 54, 2329-2336. (20) Chorover, J.; Sposito, G. Geochim. Cosmochim. Acta 1995, 59, 875-884. (21) Schroth, B. K.; Sposito, G. Clays Clay Miner. 1997, 45, 85-91. (22) Polubesova, T. A.; Chorover, J.; Sposito, G. Soil Sci. Soc. Am. J. 1995, 59, 772-777. (23) Spadini, L.; Manceau, A.; Schindler, P.; Charlet, L. J. Colloid Interface Sci. 1994, 168, 73-86. (24) O ¨ sthols, E.; Manceau, A.; Farges F.; Charlet, L. J. Colloid Interface Sci. 1997, 194, 10-21. (25) Bargar, J. R.; Towle, S. N.; Brown, G. E.; Parks, G. A. Geochim. Cosmochim. Acta 1996, 60, 3541-3547. (26) Bargar, J. R.; Brown, G. E.; Parks, G. A. Geochim. Cosmochim. Acta 1997, 61, 2617-2652. (27) Liang, L.; Morgan, J. J. Aquat. Sci. 1990, 52, 32-55. (28) Hunter, R. J. Introduction to Modern Colloid Science; Oxford University Press: Oxford, 1993. (29) Anderson, S. J.; Sposito, G. Soil Sci. Soc. Am. J. 1992, 56, 14371443. (30) (a) Lyklema, J. J. Colloid Interface Sci. 1984, 99, 109-117. (b) Chem. Ind. 1987, 21 (November 2), 741-747. (31) Charlet, L.; Sposito, G. Soil Sci. Soc. Am. J. 1987, 51, 1155-1160. (32) Sposito, G. The Chemistry of Soils; Oxford University Press: New York, 1989. (33) Fair, M. C.; Anderson, J. L. J. Colloid Interface Sci. 1989, 127, 388-400. (34) Sposito, G. The Thermodynamics of Soil Solutions; Clarendon Press: Oxford, 1981. (35) Mu ¨ nster, A. Classical Thermodynamics; Wiley: London, 1970. (36) Sposito, G. Soil Sci. Soc. Am. J. 1983, 47, 1058-1059. (37) Lim, C. H.; Jackson, M. L.; Koons, R. D.; Helmke, P. A. Clays Clay Miner. 1980, 28, 223-229. (38) Barrow, N. J. Reactions with Variable-Charge Soils; Martinus Nijhoff: Dordrecht, 1987. (39) Yates, D. E.; Healy, T. W. J Chem. Soc., Faraday Trans. I 1980, 76, 9-18. (40) Lyklema, J. Colloids Surf. 1989, 37, 197-204. (41) Lo¨vgren, L.; Sjo¨berg, S.; Schindler, P. W. Geochim. Cosmochim. Acta 1990, 54, 1301-1306. (42) Stumm, W.; Kummert, R.; Sigg, L. Croat. Chem. Acta 1980, 53, 291-312.
Received for review March 9, 1998. Revised manuscript received June 1, 1998. Accepted June 15, 1998. ES9802347
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