Generic NICA−Donnan Model Parameters for Metal-Ion Binding by

Josep Lluís Garcés , Carlos Rey-Castro , Calin David , Sergio Madurga , Francesc Mas , Isabel Pastor and Jaume Puy. The Journal of Physical Chemistr...
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Environ. Sci. Technol. 2003, 37, 958-971

Generic NICA-Donnan Model Parameters for Metal-Ion Binding by Humic Substances C H R I S T O P H E R J . M I L N E , * ,† DAVID G. KINNIBURGH,† WILLEM H. VAN RIEMSDIJK,‡ AND EDWARD TIPPING§ British Geological Survey, Wallingford, Oxfordshire, OX10 8BB, U.K., Department of Soil Quality, Wageningen Agricultural University, Dreijenplein 10, 6703 HB Wageningen, The Netherlands, and Centre for Ecology and Hydrology, Windermere Laboratory, Ambleside, Cumbria, LA22 0LP, U.K.

A total of 171 datasets of literature and experimental data for metal-ion binding by fulvic and humic acids have been digitized and re-analyzed using the NICA-Donnan model. Generic parameter values have been derived that can be used for modeling in the absence of specific metalion binding measurements. These values complement the previously derived generic descriptions of proton binding. For ions where the ranges of pH, concentration, and ionic strength conditions are well covered by the available data, the generic parameters successfully describe the metalion binding behavior across a very wide range of conditions and for different humic and fulvic acids. Where published data for other metal ions are too sparse to constrain the model well, generic parameters have been estimated by interpolating trends observable in the parameter values of the well-defined data. Recommended generic NICADonnan model parameters are provided for 23 metal ions (Al, Am, Ba, Ca, Cd, Cm, Co, CrIII, Cu, Dy, Eu, FeII, FeIII, Hg, Mg, Mn, Ni, Pb, Sr, ThIV, UVIO2, VIIIO, and Zn) for both fulvic and humic acids. These parameters probably represent the best NICA-Donnan description of metal-ion binding that can be achieved using existing data.

competitive adsorption (NICA) isotherm description of binding to a heterogeneous material, coupled with a Donnan electrostatic sub-model describing the electrostatic interactions between ions and the humic material. NICA-Donnan has been shown in several studies to be a versatile model capable of describing observed humic ion-binding behavior well over a wide range of conditions (5, 6). Using the collated data we derived recommended generic NICA-Donnan parameter values for proton binding to both fulvic and humic acids. In this paper we build on and extend that work by compiling a comprehensive database of literature and experimental data for metal-ion binding by humic substances. We then apply the NICA-Donnan model to combinations of the individual datasets to obtain generic descriptions of metal-ion binding for as many metal ions as possible. Where insufficient data are available to enable direct derivation of parameters, the observed trends in the fitted parameter values are used to interpolate values for additional metal ions. Finally we discuss briefly the likely validity and limitations of the resulting set of generic parameter values. The complete set of metal-ion binding data used in this paper, together with the earlier proton data, is available as Supporting Information.

NICA-Donnan Model The derivation of the NICA-Donnan model has been presented thoroughly elsewhere (3, 7, 8) and will not be repeated here. The final expression of the consistent NICA model for multicomponent competitive binding states that the amount bound, Q, of a component i, at solution concentration ci, is given by

Qi )

ni1 nH1

‚Qmax1,H‚

(K ˜ i1ci)ni1

∑

∑(K˜

[ ‚

(K ˜ i1ci)ni1 1 + [ (K ˜ i2ci)ni2

∑

Introduction Modeling of metal-ion interactions with humic substances in aquatic and soil systems can be pursued using a variety of chemical models (1-3). Application of any of these models to complex multicomponent real systems requires a set of suitable parameters to describe the binding characteristics of the individual metal ions. Explicit measurement of these binding properties is invariably difficult and is impractical within most investigations. The availability of a robust and extensive set of parameters for a given model is therefore highly desirable. In a previous paper (4) we carried out an extensive survey of available data for proton binding by humic substances and analyzed the data using the NICA-Donnan model. The NICA-Donnan model is a combination of the non-ideal * Corresponding author phone: +44 (0)1491 692249; fax: +44 (0)1491 692345; e-mail: [email protected]. † British Geological Survey. ‡ Wageningen Agricultural University. § Centre for Ecology and Hydrology. 958

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∑

(K ˜ ilci )ni1]p1

∑(K˜

[ ‚

i2ci)

ni2 p2

]

i

(K ˜ i2ci)ni2 1 + [

i

]

+ i

‚Qmax2,H‚ nH2

ni1 p1

i

i

ni2

i1ci)

∑

(1) (K ˜ i2ci)ni2]p2

i

Thus the total binding of a component is simply given by the sum of two identical binding expressions, one for each of the two site distributions considered by the NICA. Four parameters are characteristic of the humic material in question: Qmax1,H and Qmax2,H describe the maximum proton site density of the humic material for each distribution (in mol kg-1); p1 and p2 represent the widths of the distributions and encapsulate the intrinsic heterogeneity of the humic material. For each component considered, four ion-specific parameters, K ˜ i1, K ˜ i2, ni1, and ni2, are used to describe the median affinities, and nonidealities of the ion-binding to each distribution. The NICA equation describes specific binding of cations to the humic reactive sites. The aggregate, normally negative, charge on the humic substances also induces nonspecific binding which is described by the Donnan sub-model. In the Donnan model (3, 7, 9) the humic substance is assumed to behave as a gel with a homogeneous charge and potential distribution. The ratio of the accumulated concentration of counterions in the gel to that in the bulk solution defines a Boltzmann factor and hence Donnan potential. The induced 10.1021/es0258879 CCC: $25.00

 2003 American Chemical Society Published on Web 02/04/2003

local concentration of ions in turn influences the specific binding. Thus the NICA sub-model (specific binding) and the Donnan sub-model (nonspecific binding) are interrelated and must be solved simultaneously by iteration. The Donnan sub-model contains an expression for the Donnan volume, VD (L kg-1), given by the empirical relationship

log VD ) b(1 - log I) - 1

(2)

where I is the ionic strength and b is an empirical parameter describing how the Donnan volume varies with ionic strength. The value of b is adjustable within the model and is a property of the type of humic substance. Usually b is positive, indicating that the Donnan volume increases with decreasing ionic strength. A smaller b value suggests a smaller Donnan volume. For example, b values of 0.25 and 0.7, at an ionic strength of 0.001 M correspond to Donnan volumes of 1 and 80 L kg-1 respectively. For fulvic acids in particular, the calculated Donnan volumes are too large given the small size of the molecules and so the Donnan volume is also assumed to include a contribution from the diffuse double layer surrounding the particle. Therefore the relationship given by eq 2 also accounts for the expansion of the diffuse double layer in dilute solutions. For a given residual charge, the smaller the gel volume, the greater the concentration of counterions inside the gel and the greater the corresponding Boltzmann factor.

Data Collation As with the proton-binding analysis described in our earlier paper (4), the data collected for the calibration of Model VI (1) were used as the starting point for this compilation. The nomenclature system used by Tipping to identify datasets, e.g. FCa-02, has been maintained and extended. First, F or H designates a fulvic or humic acid, then the bound ion is specified, and finally a sequential number within each group is appended. The order of the sequential numbers is not significant. The datasets used by Model VI keep their original codes to facilitate cross-referencing. Following review, a total of 171 available datasets were identified, representing over 9000 individual experimental measurements, describing 23 different metal ions, and relating to approximately 70 different fulvic and humic acids (FA and HA). No available data were deliberately excluded from the listing and analysis. Details of the sources and nature of each dataset are given in Table 1. All the materials considered are isolated FAs or HAs, the majority extracted broadly according to IHSS standard procedures. We have not included data for metal-ion interactions with undifferentiated DOC (dissolved organic carbon) for example. The methods of measurement and manners of original data presentation vary considerably between studies. Preparation of the data files in a consistent manner was therefore a significant undertaking. Original data provided by the authors in digital format were used where available. Otherwise the data were transcribed from published tables or digitized from printed figures, as indicated in Table 1. In each case, the data were then converted, if possible, into standard format and units. Concentrations of bound metal ions were expressed in units of mol kg-1 of humic substance, as a function of free metal-ion concentration, proton concentration, and ionic strength (all in mol L-1). Proton concentrations generally required conversion from pH, which was carried out using the Davies equation for proton activity correction. A small number of data were for ionic strengths of >0.5, at which the Davies equation is not preferred. In these cases the activity correction built into ECOSAT (Davies-Helgeson equation) (10) was used. Using mol kg-1 for the bound fraction has the advantage that the mass of humic material is directly

measurable and model-independent. However, in many cases the data were presented in the form of an equilibrium quotient involving an apparent humic “molar” concentration based on an assessment of the density of a given type of reactive sites. These interpretations have been reversed to obtain the mass concentrations. Further processing was necessary in some instances to take account of speciation issues. Data reported as total aqueous metal concentrations or equivalent have been corrected for hydrolysis reactions to obtain the free metalion concentrations. Similarly, measurements made by ligandexchange techniques, involving acetate, morin, or other complexing ligands, have been corrected if the original authors had not already done so. All speciation calculations have been carried out using ECOSAT (10). Equilibrium constants were obtained predominantly from the compilations by Baes and Mesmer (11) for hydrolysis reactions, and Smith and Martell (12, 13) for other ligands and relevant ion-pairs such as CuNO3+. Constants for some reactions involving the lanthanide metals were drawn from the CHEMVAL database. After conversion, 124 of the datasets were in suitable format for fitting by the model. The remaining datasets were considered not suitable for one of the following three reasons. 1. The metal-ion binding experiments were expressed as a pH variation in the presence of a total amount of metal, with no direct observation of the bound and free metal-ion concentrations. Although these data can be easily fitted to the model by solving the humic complexation and aqueous speciation simultaneously using ECOSAT, it was impractical to do so as part of fitting to large aggregates of many individual datasets. 2. Data were for measurements of competitive binding where the binding of the competitor metal ion was not measured directly. This situation is similar to the issue of pH variation above, in that the individual datasets can be modeled using a simultaneous speciation calculation, but do not lend themselves to being part of a larger aggregate dataset. A few competition datasets did include explicit measurement of both competitors at each data point, and these were included in the main analysis. 3. Experiments were radioisotope studies, measured in terms of activity at “trace” concentrations, with the exact concentrations being unspecified. The data could be used by making assumptions concerning the actual concentration of the radiotracers based on quoted activities, but this was not preferred given the nonlinearity in the binding isotherms, even at low concentrations.

Strategy for Derivation of Parameters The analysis of proton binding by many different humic materials, discussed in our previous paper (4), showed that it was necessary and justified to consider FA and HA separately. Typically, FA and HA differ in both the total numbers of binding sites and in the distribution of affinities of those sites. In view of this evidence, the distinction between FA and HA has been maintained during the present analysis of metal-ion binding. The generic descriptions of proton binding which were derived included values for the maximum site densities and site distributions of typical FA and HA. These generic descriptions have been taken as fixed here and are used throughout the fitting of the metal-ion binding data. Plotting the multiple datasets for binding of a given ion on the same plot revealed that in general the binding measured for different materials by different research groups was very similar. Often the differences between diverse datasets were of the same order as, or even smaller than, the uncertainty spread of the data within individual datasets. The similarities are apparent in the plots which are shown VOL. 37, NO. 5, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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in the following sections. Such strong similarities allow considerable confidence that the formulation of generic descriptions for the metal-ion binding is a valid approach. Datasets which did show significant differences when compared to other data for the same metal are discussed individually in the relevant sections below. Given that there are inevitably some discrepancies between so many datasets, the weighting of data used during fitting is an important consideration. During fitting of the proton data it was judged that the major variation occurred between materials, and that the experimental variation was small in comparison. All the datasets were given an aggregate weighting of one, with each point carrying a weight equal to the reciprocal of the number of points in the set. Large datasets, therefore, did not carry more weight than smaller ones. For the metal-ion binding datasets, this approach is less justifiable. A large dataset, covering a wide range of conditions, provides a stiffer test of the model and should carry proportionally more influence on the final derived parameters than should a much smaller dataset of perhaps only a few observations at a single pH. Furthermore, it was also clear that some data were of higher resolution than others and accordingly merited higher weighting. The rigorous approach to weighting the data is to weight each point according to the reciprocal of the variance (σ2) in the measurement of the point (14). This information is generally not available in published datasets. The strategy used here was to make a simple, first-level approximation to the error involved in the measurements by estimating the spread of the analytical data plotted on a log-log isotherm plot. Estimating the 95% confidence margin of a best-fit curve through the center of the data range in question gives an indication of the 2σ spread of the data. A three-tier system was used. The default weighting was considered to be a 2σ spread on a log scale of 0.1 (log mol kg-1). A “good” dataset showed a spread of approximately 0.05 or less. A “poor”’ dataset showed a spread of approximately 0.2 or greater. Each point in the dataset was then given a weighting equal to the reciprocal of the 2σ spread for that dataset. Thus, in the final fitting, each point from a “good” dataset carried twice the weight of a standard point. Data from a “poor” set carried half the weight. Larger datasets carried more or less weight, depending on the adjudged quality of the data. The weights attributed to each dataset are shown in Table 1 as either 1, good; 2, default; or 3, poor. A grade 4 indicates that a serious problem was suspected with the data, and that the dataset was rejected for fitting purposes. In the NICA-Donnan model, the intrinsic heterogeneity parameters of the humic material, p1 and p2, are constant for all ions. All other parameters concerning the material (Qmax1,H, Qmax2,H, and b for both FA and HA) follow from the generic description of proton binding, but the p values cannot be resolved from analysis of proton binding alone and must be determined using metal-ion binding data. For the generic descriptions the optimum values for p (for both FA and HA) must be derived before the individual metals are considered. Data for a single metal ion would be sufficient to obtain a value, but the values are likely to be more robust if several metal ions are considered simultaneously. A combination of the data for the four metal ions with the largest, most extensive sets of data (i.e., Ca, Cd, Cu, and Pb) was used here. The range of the large datasets and the inter-relationship between p1, p2, and the respective metal-ion nonideality parameters, nM, ensured that the fitting was well constrained and that the resulting values of p had narrow confidence intervals. These fits were carried out using the generic values for the maximum site densities Qmax1,H and Qmax2,H. An alternative approach using variable values of Qmax,H was also investigated. Data for the same four metal ions were taken for those materials which also had specific proton-binding data 960

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available. It was then possible to take account of the actual maximum site densities for each material by using the semigeneric proton binding descriptions discussed in our previous paper (4). In the semi-generic descriptions, the positions and widths of the NICA site distributions were fixed at the generic values, but the Qmax1,H and Qmax2,H were determined individually for each material. These pairs of Qmax,H values were carried forward to the combination fit to determine the p values. The resulting fits were strong, but also very similar to the fits obtained when using a single pair of generic values for Qmax,H, except close to saturation at very high (and environmentally improbable) concentrations. This demonstrated that the generic metal-ion descriptions were relatively insensitive to the variation in site density, even for the weakly bound Ca, and it gave further confidence that the generic approach was valid. Using individual semi-generic values of Qmax,H (where available) clearly allows the model to be defined more precisely, but as most metal-ion data do not have associated proton data available, the generic values of Qmax,H were used for all subsequent calculations. The final generic values for p1 and p2 are given in Table 2. When the values of p are known, a full description of each metal ion requires four ion-specific parameters K ˜ M1, K ˜ M2, nM1, and nM2, representing the median affinities and nonidealities of the two NICA distributions for that metal ion. A benefit of the combination approach used to determine p1 and p2 is that a self-consistent set of parameter values for the four metal ions is also determined simultaneously. The metal ions with scantier data do not lend themselves to the large combination-fit approach, and would generally not contribute usefully to the definition of p. However, once the p values are fixed, each metal ion behaves independently and the remaining datasets can then be considered for each metal ion in isolation. An unconstrained fit of all four parameters to the entire dataset for each metal ion was used whenever possible. This was viable for the larger datasets, but as the quality and extent of the available data diminished, progressively stronger constraints were necessary. The second (high affinity) NICA distribution was always constrained before the first. Experience has shown that the highest-affinity sites in the second distribution are not always well characterized by experimental data unless the data extend to low concentrations and high pH. This was observed in the simple case of proton binding if data did not extend to pH 10 or higher, and similar effects were apparent for short ranges of metal-ion data. The issue has been discussed in detail by Dzombak et al. (15). The values of nM were constrained before the log Ks. The nonideality also requires a range of data to define it well, but the median binding affinities provide a simple measure of the binding strength which can be easily adjusted to fit limited data. In an extreme case, for example Sr binding by humic acid, where only a single experimental measurement was available, the values of n1, n2, and logK ˜ M2 were all estimated and fixed before adjusting logK ˜ M1. Three main considerations were used to guide the choice of appropriate fitting constraints: (1) known chemical similarities (e.g., Ca and Sr) where two metal ions could be expected to show similar binding behavior; (2) correlation of FA and HA parameter values for a particular metal ion; and (3) interpolation of observed trends in parameter values. The ways in which these constraints were applied for each metal ion are given in detail in the sections below. Predicting Parameters from Limited Data. Unfortunately, only around 9 or 10 metals (Ca, Cd, Cu, Pb, Zn, Co, Ni, Eu, UO2, and to a lesser extent Al) have published collections of data which can be reasonably considered extensive enough to describe the full variability of binding properly. For these metal ions, the model parameters could generally all be fitted without intervention. For all other metal

TABLE 1. Summary Details of Collated Sets of Experimental Data for Metal-Ion Binding by Fulvic and Humic Acids dataset code

material

source reference

points

weighting scorea

FAl-01 FAl-02 FAl-03 FAl-04

Suwannee River FA Radsla FA Lochard Forest FA Suwannee River FA

29 30 31 32

Fulvic Acids 101 3 14 2 59 pH data 35 2

FAm-01 FAm-02 FAm-03 FCa-01 FCa-02 FCa-03 FCa-04 FCa-05 FCa-06 FCa-07 FCa-08 FCa-09 FCa-10 FCd-01 FCd-02 FCd-03 FCd-04 FCd-05 FCm-01 FCo-01 FCo-02 FCo-03 FCo-04 FCo-05 FCo-06 FCo-07 FCo-08 FCu-01 FCu-02 FCu-03 FCu-04 FCu-05 FCu-06 FCu-07 FCu-08 FCu-09 FCu-10 FCu-11 FEu-01 FEu-02 FEu-03 FEu-04 FEu-05 FEu-06 FEu-07 FEu-08 FEu-09 FFe2-01 FFe3-01 FMg-01 FMg-02 FMn-01 FNi-01 FNi-02 FNi-03 FNi-04 FNi-05 FPb-01 FPb-02 FPb-03 FPb-04 FPb-05 FPb-06

Fjallveden FA Bersbo FA Gohy-573 FA Lake Drummond FA #2 Lake Drummond FA #3 Whitray Beck FA Armadale podzol Bh FA Armadale podzol Bh FA Armadale podzol Bh FA Laurentide FA Lochard Forest FA Broubster FA Laurentian Soil FA Oyster River FA Podzol soil FA Oregon soil FA Laurentide FA Podzol soil FA Gohy-573 FA Armadale podzol Bh FA Armadale podzol Bh FA Drigg FA Broubster FA Needle’s Eye FA Needle’s Eye Sepragen FA Laurentian Soil FA Suwannee River FA Suwannee River FA Suwannee River FA Podzol soil FA Armadale podzol Bh FA Podzol soil FA River Tamar FA Grassy Pond FA IHSS FA4 Podzol soil FA PUFA Strichen FA Suwannee River FA Armadale podzol Bh FA Aquatic FA Aquatic FA Whitray Beck FA Whitray Beck FA Soil FA Laurentian Soil FA Suwannee River FA Armadale podzol Bh FA Langford-Khan FA Armadale podzol Bh FA Whitray Beck FA Armadale podzol Bh FA Armadale podzol Bh FA Needle’s Eye FA Needle’s Eye Sepragen FA Broubster HA Laurentian Soil FA Oyster River FA Armadale podzol Bh FA Podzol soil FA Podzol soil FA River Tamar FA Podzol soil FA

33 33 34 35 35 36 37 16 38 38 31 19 6 39 39 17 40 18 34 16 41 19 19 19 19 20 20 42 43 44 45 46 47 48 49 18 50 51 52 41 53 54 55 55 56 20 20 16 57 16 36 16 16 19 19 19 20 58 16 46 58 47 18

8 9 10 30 60 42 19 10 74 87 13 54 144 223 227 96 70 10 17 10 65 75 54 94 63 167 36 237 23 69 11 43 24 15 18 15 60 56 22 54 32 13 15 17 22 89 51 10 26 10 43 10 10 52 50 50 6 60 10 41 66 23 16

2 2 2 3 2 pH data 2 3 2 2 pH data 2 2 1 1 4 2 4 3 3 tracer 2 2 2 2 3 3 2 2 1 3 2 2 2 2 2 1 1 3 tracer 2 tracer 2 2 2 3 3 3 4 3 pH data 3 3 2 2 2 3 2 3 2 2 2 2

FPb-07 FPb-08

Laurentian Soil FA PUFA

6 50

305 58

2 2

method of acquisition/comments

digitized Figure 3 digitized Figure 2 original data from Windermere digitized Figure 3, speciate hydrolysis, reject first 2 at pH 4 Table 1 tabulated in Appendix C tabulated in Appendix C data obtained from authors Table 5 tabulated tabulated original data from Windermere data obtained from authors raw data obtained from authors tabulated in article Figure 1 digitized Figure 1 Table 3 Table 4 raw data obtained from authors raw data obtained from authors raw data obtained from authors raw data obtained from authors raw data obtained from authors raw data obtained from authors digitized Figure 2, C 25 mg/L, FA 53.5% C digitized Figs 3,4 Table 1 digitized Figure 2 digitized Figure 1B digitized Figure 1 digitized from Figure 2 digitized Figure 1 raw data obtained from authors raw data obtained from authors Table 1 and Figures 5 and 7 Figures 1 & 2 raw data obtained from authors raw data obtained from authors Figure 1 raw data obtained from authors raw data obtained from authors Table 2 digitized Figure 3 Table 6 data obtained from authors Table 3 Table 2 data obtained from authors data obtained from authors data obtained from authors raw data obtained from authors digitized Figure 2 Table 1 digitized Figure 4 digitized Figure 1 digitized Figure 1C digitized Figure 1. Note: This dataset appears similar to the pH 5 data of FPb-04 raw data obtained from authors raw data obtained from authors

VOL. 37, NO. 5, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 1. (Continued) dataset code

material

FSr-01 FUO2-01 FUO2-02 FUO2-03 FUO2-04 FVO-01 FZn-01 FZn-02 FZn-03 FZn-04

Bersbo FA Drigg FA Broubster FA Laurentian Soil FA Suwannee River FA Podzol soil FA Armadale podzol Bh FA Smith Lake FA Armadale podzol Bh FA Bersbo FA

59 19 19 20 20 60 45 61 41 62

75 72 120 259 34 12 10 7 19 15

FX-01 FX-02 FX-03 FX-04

Suwannee River FA Suwannee River FA Laurentian Soil FA Suwannee River FA

64 42 6 43

14 62 42

HAl-01 HAl-02 HAl-03 HAm-01 HAm-02 HAm-03 HAm-04 HAm-05 HAm-06

Mosedale Beck HA Mosedale Beck HA Bocholt BOC 3/3.5 Gohy-573 HA Aldrich HA Bersbo HA Lake Bradford HA Lake Bradford HA Lake Bradford HA

31 31 21 65 65 33 33 66 67

58 48 24 20 20 7 4 6 32

HAm-07 HBa-01 HCa-01 HCa-02 HCa-03 HCa-04 HCa-05 HCa-06 HCa-07 HCa-08 HCd-01 HCd-02 HCd-03 HCd-04 HCd-05 HCd-06 HCd-07 HCd-08 HCm-01 HCm-02

Gohy-573 HA van Dijk HA 082 I Mosedale Beck HA Whitray Fell HA PPHA Suwannee River HA van Dijk HA 082 I Aldrich HA Aldrich HA Tongbersven Forest HA Leonardite HA PPHA PPHA RS3 HA RS4 HA Okchun soil HA PPHA RS6 HA Gohy-573 HA Aldrich HA

26 68 31 36 69 70 68 20 70 71 72 73 69 22 22 74 75 22 24 25

51

HCm-03 HCo-01 HCo-02 HCo-03 HCo-04 HCr-01 HCu-01 HCu-02 HCu-03 HCu-04 HCu-05 HCu-06 HCu-07 HCu-08 HCu-09 HCu-10 HDy-01

Gohy-573 HA Aldrich HA Leonardite HA van Dijk HA 082 I Aldrich HA Wako HA Peat soil humic acid Leonardite HA Sable silt loam HA PPHA Summit Hill HA Suwannee River HA van Dijk HA 082 I Eliot silt loam HA PUHA Tongbersven Forest HA Aldrich HA

26 76 23 68 20 78 79 72 80 69 49 70 68 81 50 71 25

HEu-01 HEu-02 HEu-03 HEu-04

EGA H1 HA Aldrich HA Podzol B1 HA Aldrich HA

82 83 84 20

962

9

source reference points

7 13 85 18 285 41 117 36 56 222 22 18 28 54 18 4 6 28 47 433 31 64 64 161 115 25 18 303 51 85 6 9 35 40 168

weighting scorea

method of acquisition/comments

Fulvic Acids (Continued) tracer Figure 1 2 data obtained from authors 2 data obtained from authors 3 raw data obtained from authors 3 raw data obtained from authors 2 3 Table 3, N. B. unexpected trend 0 Figure 3 tracer 2 digitized Figure 4, converted FA with rfm ) 1750 from Xu, see de Wit et al. 63 Competitive Systems competition Figure 10 competition competition raw data obtained from authors competition Humic Acids pH data original data from Windermere 2 original data from Windermere 2 Tables 1 and 2 2 Table 1; hydrolysis negligible 2 Table 2; hydrolysis negligible 2 2 tracer Table 1 3 Tables 4-7. Note: Table 7 at 1.0 M ionic strength, cf. limit of Davies eqn. 2 Tables 3, 4, 7, 10, 11 pH data Table 1 pH data original data from Windermere pH data data obtained from authors 1 experiments performed at Wallingford 2 pH data Table 1 3 raw data obtained from authors 3 digitized Figure 1 2 raw data obtained from authors pH data digitized Figure 4 3 1 experiments performed at Wallingford 4 Figure 3B 2 Figure 3D 3 Table 2 1 raw data obtained from authors 2 Figure 3F 2 2 digitized from Figure 3, assuming linear dependence of fluorescence on concn. 2 Tables 3, 4, 7, 10, 11 tracer Table 6 2 digitized Figures 2 and 3; see also ref 77 pH data Table 1 3 raw data obtained from authors hydrolysis 2 pH data digitized Figure 5 1 supplied by original authors 1 experiments performed at Wallingford 2 digitized from Figure 2 2 pH data Table 1 and Figures 1 and 4 1 raw data obtained from authors 1 raw data obtained from authors 1 raw data obtained from authors 2 digitized from Figure 2, assuming linear dependence of fluorescence on concn. 2 digitized Figure 4; used 0.23 g/L HA 3 digitized Figure 1 1 Table 1 3 raw data obtained from authors

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 37, NO. 5, 2003

TABLE 1. (Continued) dataset code

source reference

material

points

weighting scorea

HFe2-01 HFe3-01 HFe3-02 HMg-01 HMg-02 HMn-01 HNi-01 HNi-02 HNpO-01 HPb-01 HPb-02 HPb-03 HPb-04 HPb-05 HPb-06 HPb-07 HPb-08 HSr-01 HTh-01 HTh-02 HUO2-01 HUO2-02 HUO2-03 HUO2-04 HUO2-05 HUO2-06 HZn-01 HZn-02

van Dijk HA 082 I van Dijk HA 082 I Liu & Millero HA Whitray Fell HA van Dijk HA 082 I van Dijk HA 082 I van Dijk HA 082 I Aldrich HA Aldrich HA Leonardite HA Garcia Rodriguez HA PPHA van Dijk HA 082 I PPHA PPHA PPHA PUHA Garcia Rodriguez HA Garcia Rodriguez HA Lake Bradford HA Aldrich HA Aldrich HA Mirochov bog HA Gohy-573 HA Aldrich HA Garcia Rodriguez HA Yolo HA van Dijk HA 082 I

68 68 85 36 68 68 68 20 20 72 86 73 68 87 88 75 50 86 86 89 27 90 28 91 20 86 92 68

Humic Acids (Continued) pH data pH data 10 solubility data 11 pH data pH data pH data pH data 437 3 214 3 64 pH data 6 2 35 2 pH data 100 2 22 2 17 1 52 2 6 3 5 hydrolysis tracer 8 2 tracer 27 3 36 3 450 3 6 hydrolysis 15 2 pH data

HCaCd-01 HCdCa-01 HCuCa-01 HCdCa-02 HZnCa-01 HX-01 HX-02 HX-03 HX-04 HX-05

PPHA PPHA PPHA Tongbersven Forest HA Tongbersven Forest HA PPHA PPHA PPHA Suwannee River HA Bainsville clay loam HA

7 7 7 71 71 88 75 75 70 93

Competitive Systems 1 98 1 1 24 1 20 1 32 competition 44 competition 77 competition competition 29 competition

method of acquisition/comments

Table 1 Table 1 and Figure 4 Figures 8 and 9 data obtained from authors Table 1 and Figure 4 Table 1 and Figure 4 Table 1 and Figure 4 raw data obtained from authors raw data obtained from authors digitized Figure 3 Table 5 data supplied by authors Table 1 raw data obtained from authors Figure 2 raw data obtained from authors raw data obtained from authors Table 4 Table 7 Figure 6, assumed HA 50% C Table 2 digitized Figure 4 Tables 4, 5 and 6 raw data obtained from authors Table 6 Table 1 and Figure 4 experiments performed at Wallingford experiments performed at Wallingford experiments performed at Wallingford raw data obtained from authors raw data obtained from authors Figure 2 raw data obtained from authors raw data obtained from authors required speciation of CO3 digitized Figure 1; cocktails of 11 metals; Low bound concn. not reported.

a Weighting score indicates either the estimated standard error range (1, good; 2, default; 3, poor; 4, reject) or the reason the data were not suitable for fitting to the model in the current analysis; see the main text for complete explanation.

TABLE 2. Recommended Generic Values for the Heterogeneity Parameters p1 and p2, Obtained from Combination Fits of Metal-Ion Binding Data for Ca, Cd, Cu, and Pb, Using the Previously Established Generic Descriptions of Proton Binding p1

p2

fulvic acid 0.59 0.70 humic acid 0.62 0.41

no. of no. of datasets data 50 50

R2

2191 0.963 2118 0.954

RMSE log mol kg -1 0.203 0.198

ions, a method is needed to deduce meaningful parameters from incomplete evidence. The emergence of trends in the fitted parameter values allows the possibility of interpolation or extrapolation of some form of linear-free-energy type of relationship as a means of obtaining parameters for other metal ions. One approach is to use the variation in hydrolysis behavior of the different metal ions as an indication of likely relative capabilities for binding to humic substances. In Figure 1, the upper plots show the derived generic values for n1 and n2 as a function of the formation constants of the first hydrolysis complex (MOH(z-1)+) for each metal ion (Mz+) (11). When only the values of n1 which were freely fitted without constraint were considered, a strong correlation with the

hydrolysis constants was apparent. Furthermore, no clear differences between FA and HA could be discerned, so they were considered part of the same trend. A linear regression to the 17 best values for n1 generated the equation

n1 ) 0.14 - 0.055 log KOH

r2 ) 0.85

(3)

The strength of the correlation is sufficient that this expression can be used henceforth to obtain a value for n1 in the absence of specific data. Slightly fewer (12) freely fitted values of n2 can reliably be derived from the available data. In each case, with the exception of one outlier (Pb) which was excluded, the value of n2 lies between n1 and n1/2. Calculating the mean yields

n2 ) 0.76n1 (σ ) 0.18)

(4)

This relationship, when combined with eq 1, was therefore used to predict values for n2. For small datatsets it was thus possible to constrain n1 and n2 before fitting the values of log K. In this way generic log K values were obtained for several other metal ions represented in the compilation. Constrained parameters are italicized in Table 3. VOL. 37, NO. 5, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Relationships between the first hydrolysis formation constants (KOH) of metal ions and the fitted NICA-Donnan parameter values for binding by fulvic acids (left column) and humic acids (right column). The lines show the regressions based on values achieved using unconstrained fits to the larger datasets, as discussed in the main text, and are used as the basis for predicting parameter values when data are not available. For extremely limited data, or in the complete absence of data, it is necessary to be able to predict the values of log K1 and log K2. The values of the affinity constants in the NICA model cannot be related directly to classical constants because of the introduction of the ni nonideality exponent (3). Comparisons must therefore consider the exponentiated value Kini rather than Ki (in logarithmic notation: ni log Ki not log Ki). The two center plots in Figure 1 show that when the constants are expressed in this way, correlations with the hydrolysis formation constant are again apparent. Using those values of log K which can be derived from the observed data provides the following expressions for linear regression. 964

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For fulvic acids:

n1 log K1 ) 0.35 log KOH + 2.43

n ) 9, r2 ) 0.74

(5)

n2 log K2 ) 0.78 log KOH + 8.21

n ) 7, r2 ) 0.74

(6)

For humic acids:

n1 log K1 ) 0.26 log KOH + 2.59

n ) 12, r2 ) 0.83 (7)

n2 log K2 ) 0.41 log KOH + 4.98

n ) 11, r2 ) 0.71 (8)

FIGURE 2. Plot showing combination of all available experimental data for calcium and copper binding by fulvic acids, compared with the NICA-Donnan model description using the generic parameters given in Table 3. These relationships are plotted as lines on the center plots of Figure 1. Two further features of the consistent NICA model can be used to assess the validity of the parameter values which are obtained by fitting. First, the nature of the regression expressions derived above ensures that, according to the predicted values, n1 log K1 and n2 log K2 must also be correlated directly with each other. The two lower plots in Figure 1 show the correlation lines that would be expected, and show a reasonable agreement with the fitted parameters. Second, the ratio of nHi/nMi provides an indication of the theoretical maximum proton-metal-ion exchange ratio (3) and can itself be compared with experimental observations of binding stoichiometry. The ratios generated by the generic fits of Ca, Cd, and Cu are entirely consistent with observed exchange ratios for PPHA (3). Other examples are also encouraging. For example the larger fitted ratios of 2-3 for aluminum and iron are consistent with observed behavior for binding of these metal ions on oxide surfaces. Thus, using eqs 3-8, NICA-Donnan parameter values have been predicted for additional environmentally relevant metal ions where no experimental data are available. The values are italicized in Table 3. Undoubtedly these values should be used with caution. Further data would be required to test the predictions, refine the parameter values and increase the confidence of the descriptions. Also, there will inevitably be some instances where materials do not fully conform to the generic descriptions that can be considered to describe the behavior of a “typical” fulvic or humic acid. The sections below specify the procedures used to obtain generic NICA-Donnan parameters for each metal ion from the available datasets for fulvic and humic acids. The precise reasoning and choices of constraint during fitting, or the application of eqs 3-8 for prediction, are detailed in each case. The resulting optimum parameter values are listed in Table 3. Comparisons of the observed data and fitted model descriptions are illustrated in Figure 2 for fulvic acids, using Ca and Cu as representative examples, and in Figure 3 for humic acids, using Co and UO2 as representative examples. Parameters for Fulvic Acids. Aluminum. Three datasets were suitable for fitting (FAl-01, 02, 04) and all were used. The data did not fully constrain the model, in part because of the uncertainty margins in the experiments. In particular, the overall fit was insensitive to relatively large changes in

the parameters describing the first (carboxylic-type) distribution if the value of logK ˜ M2 was decreased dramatically. The final values used are from the point at which the sensitivity increased again. With these constrained, the other parameters converged well to give a satisfactory fit to the combined data. Americium. Three datasets were available (FAm-01-03), but they covered a very small range. Values for n1, n2, and logK ˜ M2 were estimated from the expressions in eqs 3-8, before adjusting logK ˜ M1. The resulting fit passed through the center of the data. Calcium. Data were fitted as part of the combined fit used to derive the p values. Eight datasets were in a form suitable for inclusion in the fitting (FCa-01, 02, 04-07, 09-10). Set FCa-05 (16) was inconsistent with the other sets and was omitted from the optimization. All eight of the other sets were fitted simultaneously to yield a good model fit, although it was necessary to impose constraint on the value of n2, and the value logK ˜ M2 had a wide uncertainty margin. Analysis of the NICA-Donnan speciation showed that in the concentration ranges covered by the data Ca is bound almost entirely on the sites of the first distribution. The behavior of the second distribution was hence very poorly defined, but as it contributes so little to the binding behavior the uncertainty has only minimal impact on the overall confidence of the modeling. The data and fits for all eight datasets are shown in Figure 2. Cadmium. Data were fitted as part of the combined fit used to derive the p values. Five datasets (FCd-01-05) were available for fitting. The measured bound concentrations in set FCd-03 (17) were approximately 100 times lower than for any other study, so these data were excluded. In addition, data for FCd-05 (18) were poorly resolved compared to the other high-quality data available from the same authors, so FCd-05 was also not used during fitting. The remaining datasets covered a good range of conditions. As for calcium, it proved necessary to constrain the second distribution slightly because the binding to the second distribution was weak and not well defined. A value of n2 was chosen equal to that obtained for cadmium with humic acids. With this fixed, the optimization gave an excellent fit to the full range of the data. Cobalt. Seven datasets were available in a form suitable for fitting (HCo-01, 03-08). All were used to give the VOL. 37, NO. 5, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. Plot showing combination of all available experimental data for cobalt and uranium (UO22+) binding on humic acids, compared with the NICA-Donnan model description using the generic parameters listed in Table 3. maximum range of data coverage. Some constraint of the parameters proved necessary, so n2 was fixed to be the same value as for Co binding by humic acids. Careful optimization of the other three parameters gave a reasonable fit to the full range of data. Copper. Data were fitted as part of the combined fit used to derive the p values. Eleven datasets were available (FCu01-11), covering a wide range of conditions. All were fitted without constraint, giving a robust convergence of the model, and a good description of the data, which is illustrated in Figure 2. Curium. Only one dataset (FCm-01) was available. The reported binding was much weaker than the trivalent nature of Cm3+ or the comparisons of other Cm formation constants might suggest. The fit was therefore acutely sensitive to high values of logK ˜ M2. Values of ni were predicted using the generic relationships in eqs 3-8 and the predicted value of logK ˜ M2 was reduced to the point at which the fit to the observed data became insensitive to it. LogK ˜ M1 then converged to a value indicating a much lower binding strength than for similar metal ions. Europium. Seven datasets were suitable for fitting (FEu01, 03, 05-09). An unconstrained fit converged well (R2 ) 0.951) to give realistic parameter values, in keeping with the apparent trends. The spread of uncertainty within the datasets was moderately large, but the range of data represented by the combined dataset was sufficient to define the binding well. The poorest agreement with the generic fit was observed for the two datasets describing Suwannee River FA (FEu-01 and FEu-09), but they were not excluded. Iron. One small dataset describing binding of FeII was available (FFe2-01). It was necessary to constrain the second site distribution using values predicted with eqs 3-8. The model could then be fitted to the data well by adjusting logK ˜ M1 and n1. The observed pH-dependence of the binding was smaller than predicted, resulting in a larger metal-proton exchange ratio. The only data available for FeIII were those of Langford and Khan (FFe3-01) which were measured at extremely acidic pH (1.0, 1.5, and 2.5). The quality of the data was not very good owing to the relatively low percentage of FeIII bound at these low pHs. Lead. Data were fitted as part of the combined fit used to derive the p values. Eight datasets were suitable for fitting (FPb-01-08). There were only minor differences between the sets so all were used. However, the data did not fully 966

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define the model parameters and it proved necessary to impose constraints. The values of n1 and n2 were set to be the same as achieved by free optimization for Pb binding by ˜ M2 were humic acids, then the values of logK ˜ M1 and logK optimized successfully. The resulting fit was good. Magnesium. Only one dataset (FMg-01) was available, comprising few observations. Predicted parameter values gave a model description which fell within the spread of the data. However, the data were insensitive to variation in the parameters because under the conditions measured, the NICA-Donnan model calculates the binding to be dominated by nonspecific binding in the Donnan phase, with negligible specific binding. The log K and n parameters are therefore largely untested. Manganese. One dataset was available (FMn-01) containing only a few measurements. Values of n1, n2, and log K ˜ M2 were fixed using the predictions described by eqs 3-8. The value of log K ˜ M1 was then optimized, converging to a value that was almost the same as had been predicted, and giving a good fit to the observed data. Nickel. Five datasets were available (FNi-01-05). All were fitted simultaneously. The parameter values obtained for Ni binding by humic acid were used to guide the optimization, which was stopped at the point at which the fit became insensitive to further change in the parameter values. The resulting fit described the datasets satisfactorily but not perfectly. Nevertheless, as each dataset covered only a small range of conditions, it was beneficial to include them all to provide the widest possible range. Uranium. Four datasets describing UO22+ were available (FUO2-01-04); two from each of two research groups. However, there was a significant disagreement between the data of the two groups. The bound concentrations measured for FUO2-01 and FUO2-02 (19) were lower by an order of magnitude than the binding under comparable conditions measured for FUO2-03 and FUO2-04 (20). Consequently, fitting to the data of both groups simultaneously gave a very poor fit (R2 ) 0.3) and was considered unsatisfactory. To derive the generic parameter values, the model was fitted only to the data of Glaus et al. (20) (FUO2-03 and FUO2-04). The data from this group were preferred because (a) the range of conditions covered was larger, (b) the quality of fit to these data alone (RMSE ) 0.3) was better than could be achieved to the data of Higgo et al. (19) alone (RMSE ) 0.5),

and (c) the resulting parameter values were more consistent with the general pattern. Vanadium. Only one dataset was available, for the VO2+ ion (FVO-01). The range of data was not sufficient to define the second distribution of the model, so these parameters were fixed. When the parameters for the first distribution were fitted freely the fit was insensitive to the choice of values fixed for the second distribution. Values used for logK ˜ M2 and n2 were estimated from the pattern of values and the correlations illustrated in Figure 1. Optimized values of logK ˜ M1 and n1 then gave an almost perfect fit to the data. Zinc. Two datasets were suitable for fitting (FZn-01, 04), but these represent very few data. The parameters were adjusted in small increments, starting from the values found for humic acids. The resulting fit accommodated both datasets within the experimental spread. Parameters for Humic Acids. Aluminum. Two datasets were available in a format suitable for fitting (HAl-02, 03). Set HAl-03 (21) is for undifferentiated humic substances, rather than humic acid, but the carbon content of 55.8% by mass would be high for a fulvic acid, so the material has been classified here as a humic acid. The range of the data is limited, and is insufficient to define fully all the model parameters. Values of n1 and n2 were therefore estimated so as to achieve appropriate stoichiometric exchange ratios, and the values log K ˜ M1 and log K ˜ M2 were subsequently optimized. The resulting fit reproduced the data accurately to within the range of the experimental scatter. There is also some disparity (up to 0.5 log units, a factor of 3) between the two data sets, but given the lack of further supporting data, there were insufficient grounds for rejection of either. Americium. Six datasets were suitable for fitting (HAm01-04, 06, 07). All described the same modest range of conditions, so the model could not be fully defined from the data. When n1 and n2 were constrained using eqs 3 and 4 the log K parameters fitted freely to realistic values. The quality of the fit was insensitive to the constrained values of n1 and n2 so the predictions were accepted. Cadmium. Data were fitted as part of the combined fit used to derive the p values. Seven datasets were in a format suitable for fitting (HCd-02-08), plus Cd measured in competition experiments (HCdCa-01, 02). Bound concentrations for HCd-04 (22) were an order of magnitude lower than all the other datasets, including other data presented by the authors themselves: this dataset was therefore excluded. Optimization using all the remaining data converged well to a good fit. Calcium. Data were fitted as part of the combined fit used to derive the p values. Five datasets were suitable for fitting (HCa-03, 04, 06, 07, 08), plus Ca data derived from competitive binding datasets (HCdCa-01, 02). All were fitted simultaneously without further constraint. Cobalt. Two datasets were suitable for fitting (HCo-02, 04). During unconstrained optimization of the combined data, log K ˜ M2 drifted to unrealistic values. However, analysis showed a change in sensitivity of the overall fit at a value of around log K ˜ M2 ) 1. With this then fixed, the remaining parameters converged to give a good overall fit to the full data. The fit to HCo-02 (23) was excellent (RMSE ) 0.1), but the experimental spread of data in HCo-04 (20) was of the order of 0.5 and therefore the model could not be expected to achieve a better overall fit than this. The data are shown in Figure 3. Copper. Data were fitted as part of the combined fit used to derive the p values. Eight datasets were suitable for fitting (HCu-01, 03-06, 08-10). This represented probably the most extensive aggregate dataset for humic acid of any metal. All the data were fitted without further constraint. Some of the fitted residuals were larger than for other datasets because

of the slight variations between individual datasets, but this did not undermine a strong overall fit. Curium. Three datasets were available for fitting (HCm01, 02, 03). Unusually, the three datasets were markedly inconsistent. Sets HCm-01 and HCm-02 (24, 25) showed appreciably different binding strengths. Set HCm-03 (26) presents data at constant pH over a wide range of ionic strength, but the observed ionic-strength dependence is much smaller than data for other metals suggest (e.g., HCo02; (23)). The disparities were too great for a single model description to accommodate all the data. Imposing the generic parameters estimated from the expressions in eqs 3-8 allowed HCm-02 to be described reasonably well, but the fit to the remaining data was poor. Optimizing the fits to either HCm-01 or HCm-03 forced the parameters to unrealistic values, which were rejected. The generic parameter estimates were considered to be the best achievable. Dysprosium. One dataset was available (HDy-01), but with too small a range of data to define all the parameters. Values ˜ M2 were constrained using the predictions of n1, n2, and log K from eqs 3-8. Fitting for log K ˜ M1 produced a good fit through the data. Europium. Four datasets were available (HEu-01-04). Set HEu-03 showed an isotherm which was much steeper than the majority of the data suggest, or than the model predicts. Data from HEu-03 corresponded to the other data for part of the range, but were more than an order of magnitude different at the end of the range. The data were not rejected outright, but when these data were included fitting caused the model to try to achieve parameter values that were inconsistent with the overall pattern, so they were excluded from the optimization. The fit to the other data then converged well to realistic parameters. Although the resulting model description did not reproduce the slope of HEu-03, it did pass through the center of the data range. Iron. The only dataset suitable for fitting was that of Liu and Millero (HFe3-02) in which the solubility of freshly precipitated “Fe(OH)3”, prepared using radioactive 59Fe, had been measured in 0.7 M NaCl solutions in the absence and presence of HA. Results for 25 °C were analyzed. Optimization of the data without HA gave conditional log formation constants of -2.52, -6.50, and -23.2 for Fe(OH)2+, Fe(OH)2+, and Fe(OH)4-, respectively, and 3.93 for the formation constant for Fe(OH)3(s). These values differ slightly from those of Liu and Millero - we found that it was not necessary to include the formation of Fe(OH)3(aq). The limited data could be fitted by fixing most parameters based in Figure 1 and just adjusting log K for the first distribution. This resulted in a good fit to the solubility data. Lead. Data were fitted as part of the combined fit used to derive the p values. Six datasets were suitable for fitting (HPb-02, 03, 05-08). All were fitted simultaneously, achieving a good convergence. Nickel. One dataset was available that was suitable for fitting (HNi-02). Although it contained many data, the scatter was large, and the range of conditions did not allow full definition of the model parameters. A free optimization did not converge meaningfully. The values obtained for cobalt were used as initial estimates, and the parameters were adjusted in small increments to achieve a fit that described the available data adequately within the experimental error, yet was still consistent with the pattern of parameter values obtained for other metal ions. Strontium. One dataset was available (HSr-01). The six data are for almost identical concentrations and provide a single measurement with experimental uncertainty, rather than a range of binding conditions. Hence, multi-parameter fitting was impossible. Parameter values for n1, log K ˜ M2, and n2 were predicted from chemical similarity and from the correlations illustrated in Figure 1 to be the same as for Ca. VOL. 37, NO. 5, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 3. Recommended Generic NICA-Donnan Model Parameters for Metal-Ion Binding by Fulvic and Humic Acidsa

ion-specific parameters

Fulvic Acids substrate parameters: b, 0.57; Qmax1,H, 5.88; Qmax2,H, 1.86; p1, 0.59; p2, 0.70 ion log K˜ 1 n1 log K˜ 2 n2 no. of sets no. of data H Al Am Ba Ca Cd Cm Co CrIII CuII Dy Eu FeII FeIII Hg Mg Mn Ni Pb Sr ThIV UVIO2 VIVO Zn

ion-specific parameters

2.34 -4.11 0.03 -2.6 -2.13 -0.97 -3.40 -2.64 2.8 0.26 3.14 -1.92 -1.02 6.0 3.8 -2.1 -1.55 -2.07 -1.16 -2.5 6.0 0.78 1.03 -3.84

0.66 0.42 0.54 0.90 0.85 0.68 0.43 0.71 0.35 0.53 0.58 0.47 0.30 0.25 0.32 0.77 0.72 0.65 0.60 0.85 0.26 0.44 0.66 0.67

8.60 12.16 5.8 -4.8 -3.0 0.50 6.0 -2.21 20 8.26 3.9 5.87 -1.1 36 24 -2.4 -1.1 2.03 6.92 -4.6 34 9.06 10 -0.73

0.76 0.31 0.41 0.70 0.80 0.50 0.33 0.65 0.27 0.36 0.45 0.45 0.51 0.19 0.25 0.59 0.56 0.53 0.69 0.70 0.20 0.45 0.40 0.61

2.93 -1.05 0.94 -1.1 -1.37 -0.20 2.7 -0.24 4.3 2.23 0.8 1.92 0.1 3.5 5.2 -0.6 -0.3 -0.26 1.25 -1.36 7.4 2.45 2.4 0.11

0.81 0.40 0.54 0.90 0.78 0.73 0.43 0.79 0.35 0.56 0.58 0.57 0.30 0.30 0.32 0.77 0.72 0.64 0.60 0.78 0.26 0.45 0.45 0.67

8.00 8.89 6.14 -0.7 -0.43 2.37 8.6 1.0 12 6.85 3.9 3.43 2.2 17.5 14 0.6 1.3 1.0 4.84 -0.43 20 4.81 7.7 2.39

0.63 0.30 0.41 0.70 0.75 0.54 0.33 0.66 0.27 0.34 0.45 0.36 0.50 0.25 0.25 0.59 0.56 0.55 0.69 0.75 0.20 0.32 0.34 0.27

RMSE

3 3

150 27

0.63

0.30 0.14

7 3 1 7

468 520 17 499

0.98 0.93 0.59 0.86

0.25 0.16 0.12 0.38

11 1 7 1

541 6 248 10

0.90 0.63 0.95 0.94

0.19 0.04 0.41 0.60

1 1 5 8

10 10 168 579

0.86 0.87 0.87

0.34 0.16 0.27 0.28

2 1 2

293 12 25

0.71 0.99 0.86

0.28 0.02 0.46

R2

RMSE

Humic Acids substrate parameters: b, 0.49; Qmax1,H, 3.15; Qmax2,H, 2.55; p1, 0.62; p2, 0.41 n1 log K˜ 2 n2 no. of sets no. of data ion log K˜ 1 H Al Am Ba Ca Cd Cm Co CrIII CuII Dy Eu FeII FeIII Hg Mg Mn Ni Pb Sr ThIV UVIO2 VIVO Zn

R2

2 6

72 132

0.56 0.26

0.24 0.18

5 8 3 2

546 518 23 480

0.97 0.97 0.90

0.19 0.14 1.01 0.46

8

822

0.90

0.22

4

252

0.93

0.40

1 6 1

241 232 6

0.39 0.94

0.44 0.24 0.13

3

513

0.91

0.24

2

35

0.92

0.17

a

Estimated values, used to constrain small datasets or to predict the behavior of metals without data, are shown in italics. Q values have units of equiv kg-1.

When log K ˜ M1 was fitted, it too converged to a value almost exactly the same as for Ca. The resulting model description fell through the center of the data range. Uranium. Four datasets provided data for the uranyl (UO22+) ion in a format suitable for fitting (HUO2-01, 03, 04, 05). Plotting the data on a single plot revealed that the measured binding for HUO2-01 (27) is 10 times lower than that for comparable conditions in the other datasets; this dataset was therefore excluded. It was also noted that the pH dependence of HUO2-03 (28) is poor at pH 3.4. HUO2-05 has an experimental data spread of around 0.5, which limits the RMSE that the model can possibly achieve. For the combined dataset excluding HUO2-01, the model optimization converged well to yield a good fit, within the margin of experimental uncertainty, over 16 orders of free metal-ion 968

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concentration. Agreement between measured and fitted data is shown in Figure 3. Zinc. Two datasets were suitable for fitting, one single metal (HZn-01) and one competitive experiment (HZnCa01) in the presence of Ca, but the free Ca2+ concentrations were measured and so the competition can be taken into account using the Ca parameters derived separately. The model then converged to a good fit for zinc binding over all the data.

Discussion The results of the generic fits given in Table 3 show that, where sufficient data exist to test the model properly, the NICA-Donnan model is able to describe the binding of metal ions to FA or HA well over a wide range of conditions. The

FIGURE 4. Calculated variation in metal-ion binding by the generic HA for a wide range of metal ions and at pH 4, 6, and 8. Binding of each metal ion was calculated for 10 nM free metal ion in the presence of 1 mM free Ca2+. The diagonal lines for Sr and Zn give an indication of the pH dependence of metal ion binding and implicitly of the molar H+/metal ion exchange ratio.

uncertainty margins in the generic fits, as represented by the RMSE values, vary from metal to metal and largely reflect the quality of the underlying data. Typically, the RMSE is of the order of 0.25 log mol kg-1, often better. Worse fits (e.g., RMSE ) 0.4) are almost invariably attributable to larger uncertainties in one or more of the component datasets and have been discussed for the individual cases in the preceding sections. For the most part the agreement in binding data for different materials and different experimental techniques was remarkably good. Other than the distinction between FA and HA based on proton site densities, no patterns of divergences from the model were observed which could be attributed to systematic variations in the origin, extraction, or measurement of the humic materials. In part this was due to the large scatter or internal uncertainty observed within single datasets; in part it was due to the relative lack of alternative high quality datasets to provide independent corroboration of apparent variation in binding behavior. Both of these factors are reflections of the difficulty involved in the reproducible experimental measurement of humic ion-binding, especially at the low metal concentrations which are of environmental interest. The RMSE values achieved indicate that the model is able to predict ion binding for most metal ions to within a factor of 3 (at 2σ or 95% confidence levels) over the full range observed. The representative data illustrated in the figures show that this range can be very extensive. For example, the model is successful at reproducing the observed pattern of behavior for uranyl binding to humic acid (Figure 3), with a consistent degree of accuracy, over 16 orders of metal-ion concentration, at multiple pH values, and at varying ionic strength. The model and the generic parameters also provide a description of competitive systems without further extension, as the NICA-Donnan model is inherently a competitive binding model. It has previously been used to describe competitive behavior in individual case studies with good success (3, 7). Systems involving multi-metal competition were included in the present analysis where the bound concentrations of the metal ions involved were measured independently (Table 1). A thorough examination of the ability of the suggested generic parameters to predict competitive binding in other systems is beyond the scope of

this paper, but testing the predictions requires detailed data and remains an experimental challenge. As more data become available and the model parameters are able to be further refined, it is likely that some of the larger differences between parameter values for similar metal ions (Figure 1) may be reduced. It is also likely that some of the larger differences in parameter values between FA and HA will be reduced. Nevertheless, the present sets of parameter values provide a reasonable starting point for general speciation modeling, and are almost certainly better than ignoring such interactions completely. The extent of metal-ion binding by humics varies greatly both in terms of the particular metal ion and also in terms of pH. Under similar conditions and for the generic HA (Figure 4), the alkaline earth cations are bound the least and tri- and tetravalent metal ions, such as Th4+, Cr3+, and Fe3+ are bound the most. Hg2+ is the most strongly bound of the divalent cations investigated. In nature these very strongly bound ions also tend to be strongly hydrolyzed in solution, which will limit their binding to humic materials to some extent. The pH dependence gives a measure of the proton-metal ion exchange ratio under the given conditions. For example, under the conditions given in Figure 4, the binding of Zn increases by about 1.85 log units between pH 4 and pH 8 indicating an average H+/Zn2+ exchange ratio of 0.46. The alkaline earth cations such as Sr2+ show a steeper gradient in Figure 4 indicating a lower exchange ratio, here about 0.2. The strong relationship between the extent of metal-ion binding and the tendency to hydrolyze can be clearly seen when the amount of metal ion bound to the generic HA under a given set of conditions is plotted against the average number of OH ligands bound to the metal ion in solution at pH 6 (Figure 5). The ticks on the vertical lines represent the binding at pH 4, 6, and 8, and so their separation and the overall length of the line give an indication of the pH dependence. Larger separations and a longer line mean a greater pH dependence. Even at the 10-nM reference concentration of free metal ion used in constructing Figure 5, the binding of the most strongly bound ions (Th4+ and Fe3+) is so great that the HA is approaching saturation by the metal ion. Hence, the relatively small apparent pH dependence. VOL. 37, NO. 5, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 5. Calculated variation in metal-ion binding by the generic HA as a function of the tendency of the metal ion to hydrolyze as given by the average number of hydroxyl ligands attached to the metal ion at pH 6. The three tick marks on the vertical lines indicate the binding at pH 4 (lower), 6 (middle), and 8 (upper). Detailed characterization of an individual humic material will clearly allow a more precise simulation of the metal-ion binding but at present carries a substantial penalty in time, cost, and effort. Until further data become available, the NICA-Donnan model and the generic parameter values provided here enable reasonable estimates of metal-ion binding by humic substances to be made under a wide range of environmental conditions.

Acknowledgments We are grateful to Marc Benedetti, Jette Christensen, Iso Christl, Martin Glaus, Leonard Oste, and Sandy Robertson for providing original experimental data, sometimes in advance of publication of their own papers. The work was funded by the Natural Environment Research Council (Grant GR9/3481) and the European Commission Framework IV Program (Grant ENV4-CT97-0554). C.J.M. and D.G.K. publish with the permission of the Executive Director of the British Geological Survey (NERC).

Supporting Information Available The complete compilation of data sets used for modeling in this study is available as a single combined digital file in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org. Individual data files are also available from the authors or at www.bgs.ac.uk/ humics. We welcome notification of any additional datasets for inclusion in the database.

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Received for review June 17, 2002. Revised manuscript received November 13, 2002. Accepted December 16, 2002. ES0258879

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