Environ. Sci. Technol. 2006, 40, 7473-7480
Modeling the Interactions between Humics, Ions, and Mineral Surfaces† W I L L E M H . V A N R I E M S D I J K , * ,‡ L U U K K . K O O P A L , § DAVID G. KINNIBURGH,| MARC F. BENEDETTI,⊥ AND LIPING WENG‡ Soil Quality Department, Wageningen University, P.O. Box 8005, 6700 EC, Wageningen, The Netherlands, Laboratory for Physical Chemistry & Colloid Science, Wageningen University, Dreijenplein 6, 6703 HB, Wageningen, The Netherlands, British Geological Survey, Wallingford, Oxon OX10 8BB, UK, and Laboratoire de Ge´ochimie des Eaux, Universite´ Denis Diderot-Paris 7, UMR CNRS 7154, IPGP, Case 7052, 2 Place Jussieu, 75251 Paris Cedex 05, France
Model VI and the NICA-Donnan model are two successful models presently available for describing metal ion binding by humic materials. Both models deal with the complexity of the underlying processes (intrinsic heterogeneity, partial correlation between affinity distributions, variable stoichiometry, electrostatics) in a pragmatic way. The parameters of the NICA-Donnan model and their determination are discussed. The current interpretation of the ion-specific “non-ideality” parameters, ni, found in the NICA-Donnan model, emphasizes their role in determining the stoichiometry for the competitive binding of ions. The ratio nM/nH is reflected in the corresponding exchange ratios and the pH dependence of the metal ion binding. Experimental complications occur in testing models. Although Model VI and the NICA-Donnan models have much in common, there are differences that may become more apparent as the models are more widely tested. Recently ion binding to complexes of humics and oxides has been described by combining the NICA-Donnan model (ion binding to humics) with the CD-MUSIC model (ion binding to oxides). The impact of humic to oxide binding on both cation and anion binding is briefly discussed.
Introduction The humic acid (HA) and fulvic acid (FA) fractions of natural organic matter play an important role in the binding of metal ions in geomedia like soils and surface waters (1, 2). To be able to estimate the relative contribution of natural organic matter to the binding of cations, reliable models are required for ion binding to these materials as well as to the other important reactive geocolloids such as phyllosilicate clay minerals, metal oxides, and hydroxides. These models have to be able to operate over a broad range of conditions since the ranges of pH and salt concentration and the concentrations of individual metal ions in nature are all very large. These models also have to be able to deal with the wellknown chemical heterogeneity of the HA and FA, the variable * Corresponding author e-mail:
[email protected]. † This review is part of the Modeling Natural Organic Matter Focus Group. ‡ Soil Quality Department, Wageningen University. § Laboratory for Physical Chemistry & Colloid Science, Wageningen University. | British Geological Survey. ⊥ Universite ´ Denis Diderot-Paris 7, UMR CNRS 7154. 10.1021/es0607786 CCC: $33.50 Published on Web 08/03/2006
2006 American Chemical Society
charge/potential of the molecules, competition among a wide range of ions, and a variable stoichiometry of the various binding reactions (leading to monodentate, bidentate, and tridentate species). Yet, all this complexity requires a balanced simplification in order to arrive at models that are feasible in practice. Recent discussions of a range of models can be found in the book by Tipping (1) and the review by Dudal and Gerard (3). Both indicate that the NICA-Donnan model (4, 5) and Model VI (6), which have been developed with these broad aims in mind, can describe metal ion binding to humics including competition quite successfully. Many earlier models were successful in describing small sets of observations but lacked the scope required for use under a broader range of conditions. The model parameters for NICA-Donnan and Model VI are normally derived from high-quality laboratory data for purified HA and FA. In principle, the parameters for both models can be derived from the same datasets. Fitting the two models in this way usually indicates a similar overall goodness-of-fit (4, 6). However, while the two models share many common features they are not identical and so it is possible that some of the predictions for the binding of metal ions in natural systems may give different results, particularly for complex systems that were not included in the model calibration (7, 8). Notable differences in the model structure are the manner in which the reaction stoichiometry is taken into account, the way in which the correlation between the proton and metal ion affinity distributions is dealt with, and the way in which the affinity distribution is parameterized (continuous or discrete). The NICA-Donnan approach allows for an analytical binding equation that is combined with a simple analytical Donnan model to account for the electrostatics. These equations can be incorporated in a general chemical speciation code like ECOSAT that solves a set of equations numerically. Apart from the uncertainty arising from the choice of model and its consequences, several other sources of uncertainty arise in the application of such models. Humic substances are complex mixtures of different molecules with broadly similar behavior. A model description of a specific humic substance is therefore at best describing the average particle behavior, no matter how well the humic substance is defined. Depending on the precise nature of the humic substance, its reactivity may deviate from that of other humics. However, in general, a fairly close similarity is observed for HAs and FAs and so a “generic” behavior can be defined for them along with a certain variability. This variability can be seen from the variation in the behavior of VOL. 40, NO. 24, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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individual FAs and HAs and the resulting spread in model parameter values (6, 9, 10). The use of “generic” model constants (6, 9, 10) for “unknown” humics is based on the assumption that the HA and FA in question behaves with these generic properties, or at least reasonably close to them. Reality may deviate significantly from this assumption, but the range of variability is roughly known and so could be propagated through the calculations. Acquiring datasets for the full calibration of individual humic substances is a major task and so the additional uncertainty associated with the use of generic model constants has to be balanced against the effort involved in undertaking such a set of calibrations. Humic particles also bind strongly to metal oxide and hydroxide particles. Such associations may occur as complex colloids in surface waters and soil solutions (11) and certainly do so in the solid phase of soils and sediments. The binding of metal ions to HA or FA when bound to a mineral particle may be quite different from the binding to the humics when it is not associated with such a particle (12-15). Similarly, metal ions bound directly to the mineral surface sites are affected by the presence of adsorbed humics. It is well established that ion binding to oxides is quite dependent on the electrostatic potential profile in the vicinity of the surface and that this potential profile will be strongly affected by the presence of adsorbed humics (12-16). Therefore metal ion binding to oxides will be similarly strongly affected. Metal ion binding to the adsorbed humics will also be affected by the presence of the oxide and, in turn, this will affect the adsorption of the humic. In the natural environment, metal oxide, hydroxide, and even carbonate minerals, not only provide important reactive surfaces for cations but also for anions such as sulfate, phosphate, and arsenate, etc. The binding of anions to oxide and hydroxide surfaces will also be affected by the presence of adsorbed humic substances. Therefore humics not only influence the binding of cations directly and indirectly, but also influence the binding of anions through their effect on the potential near the interface and through site competition. Modeling these ternary interactions requires not only the combination of two types of models, namely an ion binding model for oxide surfaces such as the CD-MUSIC model (17, 18) and an ion binding model for the humics such as the NICA-Donnan model, but also a model for the binding of the humics to the oxide surface. Progress in this field requires that the nature of the existing models is well understood and that their parameterization is done in the best possible way. Therefore, the focus of the first part of this paper is on ion binding to humics with a special emphasis on the NICA-Donnan model. In the second part, experimental complications in testing the model(s) are discussed. Finally, we discuss how humic substances bind to minerals, and the consequences of this for metal ion binding.
NICA-Donnan Model General Aspects. The NICA-Donnan model has been developed in a series of papers (4, 19-21). A recent review provides an overview of the model and its practical applications (5). Here we highlight its most significant features and discuss the various model parameters. The NICA model is based on the Hill equation for the local binding or complexation of ions to homogeneous subsets of binding sites. An elegant derivation of the Hill equation based on the binding polynomial can be found in Dill and Bromberg (22). The Hill equation has most commonly been applied to describe complexation and adsorption in biochemistry. The competitive Hill equation allows for an ion-specific affinity or complexation constant, Ki, and an ion-specific stoichiometry, ni. Due to the ion-specific stoichiometry the maximum binding is also ion specific. To incorporate the binding 7474
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site heterogeneity, a continuous distribution function (23, 24) is used for all the affinity constants. This implies that the affinity distributions of the different ions are fully correlated irrespective of the stoichiometry of the respective binding reactions. In the NICA equation this results in a median binding constant for each ion i, K ˜ i, and a generic parameter, p, that describes the width of the distribution function:
Qi )
() ni
nH
QmaxH ×
(K ˜ iai)ni
∑ i
(K ˜ iai)ni
( ×
∑(K˜ a ) i i
ni p
)
i
∑
1+(
(1) (K ˜ iai)ni)p
i
where Qi is the amount of ion i bound, QmaxH is the maximum possible amount of proton binding, and ai is the activity of ion i in solution. In the application of the NICA model to date, concentrations instead of activities have been used in eq 1; this is accounted for in the ECOSAT software code. As shown elsewhere (4), fully correlated affinity distributions cannot be rigorously true for bidentate or tridentate complexes. Therefore, for these complexes ni is no longer solely governed by the stoichiometry. Nevertheless, the NICA parameters identify major processes: ni primarily reflects the reaction stoichiometry, p (0 < p e 1) reflects the heterogeneity of the humic substance as seen by all ions, and the normalization factor niQmaxH/nH reflects the different binding maximum for each ion. Inclusion of the scaling term ni/nH not only makes the model thermodynamically consistent (4), but also enables QmaxH to be estimated directly by fitting the acid-base titration data to the model since in this case ni/nH is necessarily one. Electrostatics are incorporated in the model by adding a generic electrostatic affinity term to K ˜ i (25, 26). This term depends only on the “smeared-out” potential of the humic substance and on the charge number of the ions, not on specific ion or substance properties (5). The Donnan model is used for the calculation of the smeared-out potential (2, 27). The Donnan model used to date has just one adjustable parameter, the Donnan volume (4, 20). This is chosen in such a way that for very small particles it includes most of the ionic double layer. A detailed discussion of this type of electrostatic model can be found elsewhere (5, 28, 29). To be able to derive all the model parameters within reasonable uncertainties, it is necessary to have, as a minimum, high-quality data over a wide range of pH and metal ion activities. During the early stages of model development many of the experiments were concentrated on obtaining charging (titration) curves at different ionic strengths and metal ion binding isotherms at a few fixed pHs. However, other experimental designs are possible and perhaps would be more efficient in terms of parameter estimation, e.g., fewer points-per-curve with a greater emphasis on using a greater number of competitor ions and spanning a greater range of competitor concentrations. Site Densities and Heterogeneity. The basic charging of humics is due to the presence of carboxylic- (relatively low proton affinity) and phenolic-type groups (relatively high proton affinity). Heterogeneity analysis of the proton binding behavior of different kinds of humics shows that in general a wide bimodal distribution applies (1, 9, 30). Application of the NICA-Donnan model to such data results in a summation of two NICA equations with fitted values for the site densities and heterogeneities for both the high and the low affinity distributions. In most cases, because of the overlap in the distributions, it is difficult to derive accurate estimates of the site densities solely from such fitting. It is particularly difficult to estimate the abundance of the phenolic groups since their high proton affinity means that their protonation/deprotonation behavior is not shown clearly in the pH range covered
by most titrations (pH
