Forward Modeling of Metal Complexation by NOM: I. A priori

The program MetalComplex performs these calculations using AlphaStep data ..... but the latter two criteria give similar rankings: In the soil simulat...
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Environ. Sci. Technol. 2009, 43, 2838–2844

Forward Modeling of Metal Complexation by NOM: I. A priori Prediction of Conditional Constants and Speciation STEPHEN E. CABANISS* Department of Chemistry, University of New Mexico Albuquerque, New Mexico 87131

Received June 9, 2008. Revised manuscript received January 28, 2009. Accepted February 10, 2009.

An agent-based simulation of the transformations of natural organic matter (NOM) is combined with quantitative structure-property relationships (QSPRs) for conditional metal-ligand binding constants (K′ML at pH 7.0 and ionic strength ) 0.10 M) in order to predict metal binding by NOM. The resulting a priori predictions do not rely upon calibration to environmental data, but vary with the precursor molecules and transformation conditions used in the simulation. Magnitudes and distributions of K′ML are consistent with previously reported values. In a simulation starting with tannin, terpenoid, and flavonoid precursors, metal binding decreases in the order Cu(II) ≈ Al(III) ≈ Pb(II) > Zn(II) ≈ Ni(II) > Ca(II) ≈ Cd(II), whereas in simulations containing protein precursors (and thus aminecontaining ligands), Al(III) is relatively less and Ni(II) and Cd(II) relatively more strongly bound. Speciation calculations are in good agreement with experimental results for a variety of metals and NOM samples, with typical root-mean-square error (RMSE) of ∼0.1 to ∼0.3 log units in free or total metal concentrations and typical biases of 6 for heavy metals and Al(III), these ligands are expected to be largely uncomplexed by those metals in uncontaminated environments. Ligands with 5 e log K′ML e 10 are considered to have moderate strength, and their extent of complexation is expected to vary according to environmental conditions. VOL. 43, NO. 8, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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Very strong (log K′ML > 12) and very weak (log K′ML < 3) ligands are difficult to characterize experimentally in a mixture like NOM, because they present special analytical challenges. To determine a log K′ML > 12 by measuring changes in pM for a known total metal concentration requires an analytical method of unusual sensitivity, even stripping voltammetry may not be sufficient (14, 15). On the other hand, to determine a log K′ML < 3 reliably requires that the metal be soluble enough to obtain pM of 4 or smaller, which is not the case for Al(III) and many transition metals at neutral pH. However, very weak ligands are unlikely to complex appreciable amounts of metal and very strong ligands are likely to be completely complexed regardless of whether the log K′ML is 13 or 15 or 17, so these analytical problems are not a serious concern when modeling environmental speciation. Nonetheless, they can be predicted by the a priori model presented here. Finally, it is important to note that the binding strength of a ligand molecule varies with the metal considered. For example, the “hard” diphenolic ligand molecule catechol has moderately strong binding for Al(III) and Cu(II) (log K′ML ≈ 8 and 6, respectively), but a very weak ligand for the “softer” Cd(II) and Ni(II) ions (log K′ML ≈ 1) (21). In contrast, the amino acid asparagine binds Cu(II) (log K′CuL ≈ 6) more strongly than either Ni(II) or Al(III), which have log K′ML ≈ 4 and 3.5, respectively. Thus, depending on the molecules present in an NOM assemblage and their ligand groups, it is possible to obtain a unique distribution of sites for each metal considered. The range, magnitude, and distributions of a priori predicted log K′ML values for the seven metals considered are consistent with experimental results, as shown in Figures 1 and 2 and Table 1. Large fractions of weak ligands are predicted for all metals, and many of these are very weak ligands. Except for Ca(II), all the metals have detectable fraction of strong sites in the water simulation, and Al(III) and Cu(II) have strong sites in the soil simulation as well. Although most experimental methods are capable of examining only a few orders of magnitude variation in [Mn+] (22), studies combining different methods have obtained log K′ML values ranging from the weak (10), consistent with these simulation results (23). Experimental studies typically indicate a preponderance of weak binding sites over stronger ones; however, under low metal:DOC ratios typical of environmental conditions, the latter dominate metal binding. Table 1 shows a great excess of weak sites and only a small fraction, typically ,10%, of strong sites, (log K′ML > 10). This pattern is observed for both the soil and water simulations, although the percentage of strong sites is higher for the latter. The log K′ML distributions are multimodal, with discrete “peaks” at both higher and lower binding strengths (Figures 1 and 2). The discrete nature of the site distributions is noteworthy- for example, very few molecules have Cu(II) binding sites with log K′CuL between 5 and 6, whereas an appreciable fraction have log K′CuL between 4 and 5 and between 6 and 7 (Figure 1b). This is not an artifact of the bin boundaries for the histogram, but instead indicates clustering in the estimated K′ML values, which are a strong function of the number of ligand groups in each molecule. The log K′ML distributions predicted are clearly more discrete than the continuous distributions used in the NICA-Donnan and Gaussian models (8, 24), and are less symmetrical than the discrete distributions used in the WHAM model (7). The “spikes” in site density for the heavy metals near log K′ML 6-7 in soil simulations and log K′ML 10-11 in the water simulations correspond to molecules with 6 ligand groups. In general, the water simulation (which used protein molecules as precursors) produced stronger metal binding than the soil simulation, which lacked nitrogen-containing 2840

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FIGURE 1. Distributions of binding site log K′ML values in a simulated soil NOM for (a) Al(III) and Ca(II), (b) Cu(II), Ni(II), and Pb(II), and (c) Cd(II) and Zn(II). Bins are intervals of 1 log unit: 0-1, 1-2, 2-3, etc. precursors. The simulated soil NOM has a small number of strong binding sites for Al(III) and Cu(II) (∼1% or less) and ∼16% moderate binding sites (5 < log K′ML < 10) for those metals and for Ni(II), Pb(II) and Zn(II) (Table 1). Ca(II) and Cd(II) both have 97% weak sites (log K′ML < 5). The water simulation produced many more strong binding sites (∼10% in each case) for the heavy metals Cu(II), Ni(II), and Pb(II) than for the other metals, although only Cu(II) has a much higher level of moderate binding sites as well (Figure 2). Cd(II) and Zn(II) are much more strongly bound in the nitrogencontaining NOM than in the soil NOM, with >2% strong sites and >10% moderate sites for each metal. Ca(II) is also significantly more strongly bound than in the soil simulation, although the strongest binding sites are much weaker (>5 log units) for Ca(II) than for other metals (Figure 2). Al(III) shows the smallest increase in the average log K′ML relative to the soil simulation, with fewer strong binding sites than any other metal except Ca(II). Comparing Predicted Speciation with Experiment. To assess the “reasonableness” of the a priori model predictions, we compared calculated speciation (pM versus pMTotal, where pM ) -log [M] and pMTotal ) -log MTotal) with previously published results for six metals studied at or near I ) 0.1 and pH 6.0-8.2 (Table 2). No suitable Al(III) binding data were found, perhaps because Al(III) complexation is frequently

TABLE 2. Comparing Soil Simulation with Experimental Speciation (I = 0.1) metal

NOMa

pH

Ca(II) Ca(II) Cd(II) Cd(II) Cu(II) Cu(II) Ni(II) Ni(II) Pb(II) Pb(II) Zn(II) Zn(II)

LD FA SR HA PP HA OS HA SR FA LG NOM Br HA NE FA OR FA AL NOM Be FA RO NOM

7.0 8.2 6.0 6.0 7.0 8.0d 6.6-6.9 6.9 6.0 7.0d 6.8-7.0 7.0d

DOC N RMSE 666 500 100 101 18.7 3.5 20.0 20.0 31.3 4.6 1084 10.0

8 18 60 10 30 12 10 10 11 8 2 22

0.11c 0.14 0.18 0.11 0.10 0.14c 0.24 0.10 0.15 0.31 0.01c 0.08

bias +0.11c -0.06 +0.12 -0.02 +0.06 -0.01c -0.22 -0.02 +0.13 -0.17 -0.01c +0.01

ref. methodb (25) (26) (27) (28) (29) (13) (30) (30) (31) (32) (33) (34)

ISE ISE ISE UF ISE CSV IE IE ISE CSV IE ASV

a LD ) Lake Drummond, SR ) Suwannee River, PP ) purified peat, OS ) Okchun Soil, LG ) Lake Greifen, Br ) Broubster, Be ) Bersbo, NE ) Needle’s Eye, OR ) Oyster River, AL ) Alpine Lake, RO ) reverse osmosis isolates from Edisto River and from Moose Lake. b ISE ) ion selective electrode potentiometry, ASV ) anodic stripping voltammetry, CSV ) cathodic stripping voltammetry, IE ) ion exchange, UF ) ultrafiltration. c Comparison with the 1.2% N data set made by combining soil and aquatic simulations. d I < 0.1.

FIGURE 2. Distributions of binding site log K′ML values in a simulated aquatic NOM for (a) Al(III) and Ca(II); (b) Cu(II), Ni(II), and Pb(II); and (c) Cd(II) and Zn(II). Bins are intervals of 1 log unit: 0-1, 1-2, 2-3, etc.

TABLE 1. Log K′MLi Summary Statistics Metals statistic

Al(III) Ca(II) Cd(II) Cu(II)

Ni(II)

Pb(II) Zn(II)

mean 2.47 strong meana 7.57 maximum 15.5 % weakb 83.5 b % moderate 15.3 % strongb 1.1

Soil Simulation 1.24 0.96 2.77 4.86 4.79 7.27 6.0 6.0 11.3 97.4 97.4 83.3 2.6 2.6 16.3 0 0 0.4

1.98 6.20 6.3 84.1 15.9 0

2.10 7.25 9.5 83.6 16.4 0

2.08 6.21 6.5 84.1 15.9 0

mean 3.02 strong meana 8.54 maximum 12.8 % weakb 84.1 b % moderate 13.8 % strongb 2.0

Water 2.47 5.42 9.5 94.8 5.2 0

3.44 11.05 16.8 84.0 8.2 7.9

4.48 11.83 18.5 76.3 13.7 10.0

2.92 9.02 14.2 86.4 11.0 2.6

Simulation 3.22 3.84 8.71 11.52 15.3 15.6 86.3 62.8 11.3 27.3 2.4 9.9

a Mean of the strongest 10% of sites. b Weak indicates log K′MLi < 5; moderate, 5 < log K′MLi < 10; strong, log K′MLi > 10.

studied in systems of low pH and ionic strength. Many of the humic and fulvic acid data sets used were compiled by Milne,

et al. (10), although some unfractionated NOM experiments were also included. For data sets in ref 10 that did not include a DOC value, a value was assumed and pMTotal calculated on the basis of the normalized bound metal data. Most experiments used electrochemical methods (direct potentiometry or stripping voltammetry), although some employed separation methods (ultrafiltration or ion exchange resins). Speciation was calculated as described above using the simulated soil NOM (no nitrogen) and combined aquatic and soil NOM (1.2% nitrogen by weight). Both visual and statistical comparisons indicate that the a priori predictions of metal speciation are plausible. Figure 3 shows model predictions for some of the data sets in Table 2, one for each metal ion listed. The model predicts very weak binding in some cases, with pM - pMTotal below 0.2 log units (e.g., at high total concentrations of Ca(II) and Cd(II), panels a and b in Figure 3). For Cu(II), Ni(II), and Pb(II) at lower total metal concentrations, the binding is stronger, with pM-pMTotal greater than 1 (>90% of the metal is complexed by NOM). Agreement is good even in cases where pM varies by >3 log units. Table 2 also presents two comparison statistics, the root-mean-square error (RMSE) in calculated pMTotal and the average bias, calculated as the average difference between experimental and predicted pMTotal. RMSE values are typically between 0.1 and 0.2 log units, indicating good agreement comparable to that obtained with the extensively calibrated NICA-Donnan model (10). Similarly, overall bias is low with a nearly even split between high and low biases and average absolute values of bias near 0.1 log units. The worst agreements between prediction and experiment are for Pb(II) binding by NOM from an alpine lake (RMSE ) 0.31, bias -0.17) and for Ni(II) binding by Broubster HA. The former is a whole water sample of low ionic strength that contains other metal ions that may complex some of the binding sites (32); this simulation included 0.25 mM [Ca2+] to partly account for this competitive binding, but may have omitted important trace metal competition. The Broubster HA data was collected under the same conditions as the Needle’s Eye FA data (30), which are better described by the a priori predictions (Figure 3d). The very small (N ) 2) data sample for Zn(II) binding by Bersbo FA is taken from a pH titration experiment (31); only the data near pH 7 are considered here. VOL. 43, NO. 8, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. Comparison of experimental data (discrete points) and a priori model calculations (curve) for (a) Ca(II) (26); (b) Cd(II) (27); (c) Cu(II) (29); (d) (Ni) (30); (e) Pb(II) (31); and (f) Zn(II) (34). These comparisons with experiment are intended to establish plausibility, not rigorous predictive ability. Indeed, the variation in predicted K′ML distributions with nitrogen content means that no rigorous test is possible without knowing the nitrogen content of the NOM being simulated. The fact that 9 of 12 data sets in Table 2 are well-described by the simulated soil NOM (no nitrogen) may simply result from the relatively high metal:DOC ratios employed, which minimizes the importance of the very strongest binding sites. The lowest metal:DOC ratio data sets (Cu(II) in Lake Greifen, Zn(II)-Bersbo FA) were significantly better described using simulated NOM with 1.2% nitrogen. Interestingly, stripping voltammetry and diffusive gradient thin-film Cu(II) data collected from low Cu:DOC freshwaters were poorly described by the WHAM and NICA-Donnan models (35), which have been calibrated principally using higher Cu:DOC data (10). Although the solution conditions (pH 7.8-8.5, I unknown) are not those used in the QSPRs, predicted speciation using the a priori model with 1.2% nitrogen is much closer to the experimental data than the predictions of WHAM or NICADonnan, although predictions using the simulated soil (no nitrogen) NOM are comparable to the predictions of those models. Agreement between experiment and a priori prediction is surprisingly good, and comparable to that obtained with models calibrated on metal-NOM data for these conditions (pH 7, I ) 0.1). This result suggests that the a priori model can be used to provide some insight into NOM binding sites for different metals, at least in the neutral pH range. 2842

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Relative Binding Strengths of the Metals. Does the a priori method presented here correctly predict the relative complexation strengths of metal ions at pH 7.0 and I ) 0.1? This apparently simple question is actually quite slippery, because there is no single accepted method for comparing binding strength for different metals for a complex mixture such as NOM. While an exhaustive review of this literature is beyond the scope of this article, the relative “ranking” of metals by binding strength depends somewhat on the specific conditions considered, pH, metal:ligand ratio, etc., and may depend upon the origin and isolation method of the NOM sample. Comparing log K′ML values appears simple, but it is not clear what “average” value to compare for a complex mixture such as NOM. Three possibilities are to compare (a) the mean log K′ML for all molecules, (b) the mean log K′ML of some fraction of the molecules (for example, the “strong mean” in Table 1 is the average of the strongest 10% of the molecules), or (c) the percentage of molecules above some minimum (e.g., the numbers of strong and moderate binding sites in Table 1 are those with log K′ML > 5). The first of these gives a large “weight” to the environmentally insignificant weak sites, but the latter two criteria give similar rankings: In the soil simulation, binding strength decreases in the order Cu(II) ≈ Al(III) ≈ Pb(II) > Zn(II) ≈ Ni(II) > Ca(II) ≈ Cd(II), whereas in the aquatic simulation, it decreases in the order Pb(II) ≈ Cu(II) > Ni(II) > Zn(II) ≈ Cd(II) ≈ Al(III) > Ca(II). An alternative method compares the calculated speciation of each metal under identical conditions, similar to the

ionic strength values, and (c) expanding the model to include additional metals ions such as Hg(II) and UO(VI), part II of this work will explore the mechanistic predictions of the a priori model, including the ’hard” and “soft” nature of binding sites, competition among metal ions, and correlation of metal binding with bulk NOM properties like molecular weight and aromaticity.

Acknowledgments This work was supported by the National Science Foundation through the NSF Information Technology Research initiative and the Division of Environmental Biology via Grant NSF DEB 0113570. Three anonymous reviewers provided useful and thought-provoking comments that helped improve the manuscript. FIGURE 4. Calculated pM in solutions of 10.0 mg C/L and pMTotal ) 6.0 at pH 7.0 and ionic strength 0.10 M using NOM from the soil simulation (0% N) and a mixture of soil and water simulations (1.2% N). comparison in Milne, et al. (10). Figure 4 shows calculated pM for the simulated soil (no nitrogen) and mixed soil and water (1.2% nitrogen) data sets in solutions of 10.0 mg C/L and 1.00 µM MTotal. For the soil simulation data set used for comparison with most of the experimental data in Table 2, the metal binding strength decreases in the same order given above, Cu(II) ≈ Al(III) ≈ Pb(II) > Zn(II) ≈ Ni(II) > Ca(II) ≈ Cd(II).Inthe1.2%nitrogendataset,therankingchanges-Cu(II) and Pb(II) are still the most strongly bound, followed by Ni(II), but Al(III) binding is only slightly stronger than Zn(II) and Cd(II), which is much more strongly bound than Ca(II). These model results are generally consistent with experimental comparisons. Typically, Ca(II) binding is weaker than that of heavy metals, but is rarely measured in the same systems (24). Direct comparisons have typically focused on heavy metals that are amenable to similar analytical methods (36-38). Christl et al. (36) found using voltammetric methods that Cu(II) and Pb(II) have similar complexation with FA and with HA at pH 6 (difference Zn(II) ≈ Cd(II). Saar and Weber (38) found Cu(II) > Pb(II) . Cd(II) at pH 6 using ion selective electrodes at high metal concentrations. Although it is a generalization, these comparisons suggest that heavy metal binding to various NOM samples decrease in the order Cu(II) >≈ Pb(II) > Ni(II) > Zn(II) ≈ Cd(II), similar to the a priori predictions. Although direct experimental comparisons are restricted by practical considerations, model calculations have no such limitation. According to the NICA-Donnan calculations of Milne, et al. (10), binding by ‘generic humic acid’ in the presence of 1 mM free Ca2+ decreases in the order Al(III) ≈ Cu(II) > Pb(II) > Zn(II) > Ni(II) ≈ Cd(II) at near neutral pH. This order is generally consistent with the direct experimental comparisons, except that Zn(II) binding is notably stronger relative to Ni(II) and Cd(II) in the model predictions than in the direct comparison by Christensen and Christensen (37). The NICA-Donnan predictions are also consistent with the a priori predictions presented here, except the relative strength of Zn(II) and Ni(II). Only sparse Zn(II)-HA binding data (and limited Zn(II)-FA data) were available for calibrating the NICA-Donnan model (10), so it is unclear whether this difference is significant. Future Work. Having established that AlphaStep simulations coupled to empirical QSPRs (the a priori model) can make quantitative predictions about metal complexation under restricted (pH 7.0, I ) 0.1) conditions, logical next steps are (a) using the model to gain mechanistic insight into nature of metal-NOM interactions, (b) adding acid-base and electrostatic terms to permit extension to other pH and

Appendix A Abbreviations aj Bias #Ci CTotal DOC FA, HA I K′MLi [L′i] LTotal,i [M] [MLi] MLTotal MTotal N NOM pH pM pMTotal QSPR RMSE xi,j

coefficient for the jth descriptor in the QSPR average absolute value of the differences between experiment and model number of C atoms in the ith molecule of a data set total number of C atoms in a data set dissolved organic carbon in mg C/L fulvic acid, humic acid ionic strength (molar units) conditional formation constant for complex MLi from M and L′i molarity of uncomplexed ligand (ith molecule of N) summed molarity of all forms of the ith molecule molarity of uncomplexed metal ion molarity of metal complexed with ith ligand summed molarity of all MLi summed molarity of all forms of metal, free and complexed number of molecules in a data set natural organic matter -log {H+} -log [M] -log (MTotal) quantitative structure property relationship root-mean-square error the jth descriptor variable for the ith molecule

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