Environ. Sci. Technol. 2001, 35, 2049-2059
Generic NICA-Donnan Model Parameters for Proton Binding by Humic Substances C H R I S T O P H E R J . M I L N E , * ,† DAVID G. KINNIBURGH,† AND EDWARD TIPPING‡ British Geological Survey, Wallingford, Oxfordshire, OX10 8BB, U.K., and Centre for Ecology and Hydrology, Windermere Laboratory, Ambleside, Cumbria, LA22 0LP, U.K.
Forty-nine datasets consisting of literature and experimental data for proton binding by fulvic and humic acids have been analyzed using the NICA-Donnan model. The model successfully described the behavior of the individual datasets with a high degree of accuracy and highlighted the differences in site density and binding affinity between fulvic acids (FA) and humic acids (HA) while demonstrating their strong similarities. The data have also been used to derive generic model descriptions of proton binding by FA and HA that can be used for modeling in the absence of specific parameter sets for the particular humic substance of interest. These generic parameters can provide estimates of the amount of proton binding by a wide variety of humic substances to within approximately (20% under any given conditions. The maximum site density for protons was 7.74 and 5.70 equiv kg-1 for a generic FA and HA, respectively. The recommended generic NICADonnan parameter values for FA are b ) 0.57, Qmax1,H ) 5.88, log K˜ H1 ) 2.34, mH1 ) 0.38, Qmax2,H ) 1.86, log K˜ H2 ) 8.6, and mH2 ) 0.53; for HA the values are b ) 0.49, Qmax1,H ) 3.15, log K˜ H1 ) 2.93, mH1 ) 0.50, Qmax2,H ) 2.55, log K˜ H2 ) 8.0, and mH2 ) 0.26.
Introduction The influential role of humic substances in controlling the mobility and bioavailability of metal ions in aqueous environmental systems is well-known and has been extensively studied. Despite this attention, the ion-binding behavior of the humics remains difficult to describe and model because of the heterogeneity of the humic materials and because the ion binding is dependent on many environmental variables (pH, ionic strength, metal-ion concentration and speciation, presence of competing ions). Over the past few years, two models have emerged which show encouraging success at describing humic ion-binding behavior over a wide range of conditions and metals: Model VI and NICA-Donnan. Model VI is a discrete site model, while the NICA-Donnan model is a continuous distribution model (1). Model VI (2) builds on a series of progressively more sophisticated models, each with a wider scope and subjected to more extensive calibration against literature data (3-5). * Corresponding author: phone: +44 (0)1491 692249; fax: +44 (0)1491 692345; e-mail:
[email protected]. † British Geological Survey. ‡ Centre for Ecology and Hydrology. 10.1021/es000123j CCC: $20.00 Published on Web 04/14/2001
2001 American Chemical Society
Model VI has been applied to the largest range of data of any humic ion-binding model to date. However, such is the rate of work in the subject that significant new datasets have become available even since Model VI was published. Development of the NICA (non-ideal competitive adsorption) family of models has included extensive testing and calibration against a large body of experimental data collected specifically for the purpose using a purified peat humic acid (PPHA) (6-8). The Consistent NICA-Donnan model (or NICCA-Donnan model) is the latest and most rigorous version. It combines thermodynamic consistency in its treatment of competitive adsorption with a Donnan description of the electrostatic behavior of the humic particle. The consistency affects only the description of competitive or multicomponent binding. For proton binding in the absence of specific metal-ion binding, the NICCA and original NICA models are identical (8). Although the Consistent NICADonnan model has shown itself to be capable in several studies (9-11), it has so far not been applied to the full range of literature data. At present, usable parameter values are only available for the limited range of materials against which the model has already been tested. One of the problems facing anyone who wishes to apply these models to a real system involving humics is that characterizing the materials is often difficult, time-consuming, and expensive. In most cases the costs of this are prohibitive. There is therefore a need for an ‘off-the-shelf’ set of parameters that can be used in modeling proton and metal-ion interactions of the humic material of concern. The description should be sufficiently accurate and versatile to enable usable modeling without detailed characterization; yet it should also be flexible enough to accommodate as much as possible of the available information about the specific humic material. Tipping has produced such a set of parameters for both humic and fulvic acids for Models V and VI (2, 5). Here we derive a similar set for proton binding based on the NICA-Donnan model. Using the datasets analyzed by Tipping as a starting point, we have compiled a comprehensive database of humic ionbinding data from the literature. In this paper we present and discuss the available data for proton-binding by humic and fulvic acids. We then apply the NICA-Donnan model to the proton-binding data and so obtain a general-purpose description of proton binding. We also discuss the limitations of such an approach. In addition, by making the database openly available, we aim to provide a useful resource for others.
NICA-Donnan Model The theory of the NICA-Donnan model has been presented in detail elsewhere (1, 7, 8). Here it is sufficient to state that using the NICA equation, the amount of protons bound, QH, is given by
(K ˜ H1[HS])m1 (K ˜ H2[HS])m2 QH ) Qmax1,H‚ + Q ‚ max2,H 1 + (K ˜ H1[HS])m1 1 + (K ˜ H2[HS])m2 (1) where the suffixes 1 and 2 denote that a double site distribution is used. Qmax,H is the total number of available proton binding sites within each distribution, K ˜ H is the median value of the affinity distribution for protons, [HS] is the concentration of protons at the surface of the humic particle, and m defines the width of the distribution. The mi are a measure of the apparent heterogeneity of the humic subVOL. 35, NO. 10, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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stance. When metal-ion binding data are available, m can be split into an ion-specific component and a substrate-specific component, but when only proton data are available, this separation is not possible. Thus, a full NICA description of proton binding by a humic material includes the following: two parameters, Qmax1,H and Qmax2,H to describe the site density of the humic material for protons (in mol kg-1) and four proton-specific parameters, K ˜ H1, K ˜ H2, mH1, and mH2, to describe pH-dependent binding. After the specific binding of protons has been taken into account, humic substances normally have a residual net negative charge. This charge is neutralized by the nonspecific binding of counterions. In the Donnan model (7, 8, 12), it is assumed that the humic substance behaves like a gel with a uniform, smeared-out distribution of charge and potential within the gel. The net negative charge attracts an excess of cations (Na+, H+, Ca2+, etc.), and the ratio of the concentration of cations in the gel to that in the bulk solution defines a Boltzmann factor and a corresponding Donnan potential (7). The locally enhanced concentration of protons in the gel, [Hs], is also used to calculate the specific binding of protons using eq 1. There is therefore some feedback between the specific binding (NICA model) and the nonspecific binding (Donnan model), and the two have to be solved simultaneously and iteratively to give the unknown Boltzmann factor. Each point on a titration curve has a different Boltzmann factor. Typically, it varies between 10 and 100, which implies that the acidity in the gel phase is 1-2 pH units lower than in the bulk solution. A critical parameter in the Donnan model is the Donnan volume, VD. This is assumed to follow the following empirical relationship
log VD ) b(1 - log I) - 1
(2)
in which I is the ionic strength and b is an empirical parameter describing how the Donnan volume varies with ionic strength. Normally b is positive, which implies that the Donnan volume increases with decreasing ionic strength, i.e., there is some swelling in dilute solutions. For FAs 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. A large Donnan volume of, for example, 80 L kg-1 at an ionic strength of 0.001 M corresponds to a b value of 0.7, whereas a smaller Donnan volume of 1 L kg-1 at the same ionic strength would give b ) 0.25. The value of b, like Q, is a property of the type of humic substance.
Data Collation All available published and unpublished data have been included in the database. No data were deliberately omitted. Nineteen sets of data for proton binding had already been collected for use with Model VI (2), and these formed the foundation of the present work. After completing a review, a total of 49 datasets were identified. To provide consistency, the system used to identify datasets is exactly the same here as that used during discussion of Model VI (2), e.g., FH-03 or HCa-02. The first letter denotes a humic (H) or fulvic (F) acid; the second letter denotes the ion of interest (in this paper exclusively the proton, H), and the numbers are then sequential within each subset. Datasets used by Model VI retain their original codes. 2050
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Details of the sources and nature of each dataset are given in Table 1. Where possible, raw data in electronic format were obtained directly from the original authors. Otherwise, the data were obtained by scanning and digitizing the published data as accurately as possible. In some cases, the data used for Model VI were subsets of the full data, achieved by omitting alternate (or more) points in order to obtain balanced numbers of data points for optimization and fitting. The software used in this work did not have the same constraints regarding numbers of data points, so these data were redigitized to generate the full datasets. All the data have been converted to a standard format and units, so that they are expressed as charge on the humic material (equiv kg-1) as a function of ionic strength and bulk proton concentration (mol L-1). Charge per kilogram is preferred to molar quantities for the humics because the molecular weight of humic substances is often a subjective value dependent on the method used to estimate it, whereas mass is usually measured directly. Where necessary, results expressed in molar quantities were converted to mass quantities using the authors’ stated figures for the molecular weights. Proton concentrations have been derived from pH measurements using the Davies equation for estimating the proton activity coefficient. Derived data, such as those expressed in terms of equilibrium constants and which are necessarily model dependent, have been processed by reversing the authors’ own calculations. Figures 1 and 2 show all 49 datasets presented in identical format, enabling easy visual comparison of the different experiments. Most of the data were obtained by potentiometric titration. Analytical errors (in terms of protons bound) inherent in such titrations increase exponentially at pH values below around 3.5 or greater than about 10.5, making reliable measurements at the ends of the pH range extremely difficult. Most authors therefore quote data in the range pH 3.5-10.5; some have conducted measurement only in the acid region, with data up to pH 7 or 8 (Table 1). The range of ionic strengths used in the data is generally good. Most datasets include data for at least three salt strengths, varying by at least a factor of 10. Some cover wider ranges. Only three of the 47 sets considered were restricted to single ionic strengths (FH-06, FH-07 and HH-02) and hence did not permit intraset calculation of the salt-dependence of the proton binding. Determination of the initial charge during titration (discussed, for example, by Westall et al. (33) and Avena et al. (25)) leads to some difficulties in critically assessing the quality of datasets. Proton binding data is usually quoted in terms of the absolute charge on the material. In principle, the absolute charge can be calculated by a simple charge balance based on knowledge of the amount of pure humic and the quantities of titrants added to an experiment. However, the approach relies on accurate knowledge of the purity of the humic substance concerned and such details are not always presented in the original publications. A number of authors do quote the ash residue content of their materials, although rarely with elemental analysis of the ash. Some are evidently highly pure, with ash contents of 2% (e.g., HH-08, HH-10, HH-20). As an indicator of the potential impact of this impurity on the charging curves, if it was assumed that a 1% ash content was due entirely to Ca bound to the humic material, this would correspond to an initial negative charge on the humic of 0.5 equiv kg-1 or around 10-20% of the total titratable charge in some cases. In the absence of full details of the initial charge estimation and correction, it was necessary to accept the data as presented but to remember the possibility of uncertainty in the absolute humic charge.
TABLE 1. Summary Details of Collated Sets of Experimental Data for Proton Binding by Humic and Fulvic Acids dataset
material
ref points
FH-01 FH-02 FH-03 FH-04
Lake Drummond FA Lake Drummond FA Suwannee River FA Bersbo FA
13 13 14 15
FH-05 FH-06 FH-07
Gota River FA Satilla River HS Gota River FA-1
16 17 18
45 0.01-1.0 39 0.1 41 0.1
FH-08 FH-09
Lochard Forest HA Lake Drummond FA
3 19
81 0.001-0.1 223 0.001-0.5
FH-10 FH-11 FH-12
Whitray Beck FA 20 Suwannee River FA 21 Armadale podzol Bh FA 21
72 0.003-0.1 98 0.001-0.10 255 0.001-0.10
FH-13 FH-14 FH-15 FH-16 FH-17 FH-18 FH-19 FH-20 FH-21 FH-22 FH-23 FH-24 FH-25
Gota River FA Laurentian Soil FA Suwannee River FA Tuse FA Skagen FA Vejen Landfill L1 FA Vejen Landfill L2 FA Derwent FA Kranichsee FA Laurentian Soil FA Laurentian Soil FA PUFA Strichen FA
21 22 22 10 10 10 10 23 24 25 11 26 39
118 208 194 620 588 602 591 869 663 249 255 117 662
HH-01 Peat soil humic acid
27
40 0.033-2.0
HH-02 Urrbrae loam humic 11 HH-03 Leonardite HA
28 29
14 0.1 79 0.001-0.2
HH-04 Mosedale Beck HA HH-05 van Dijk HA
3 30
36 0.001-0.1 56 0.025-2.0
HH-06 HH-07 HH-08 HH-09 HH-10 HH-11 HH-12 HH-13 HH-14 HH-15 HH-16 HH-17 HH-18 HH-19 HH-20 HH-21 HH-22 HH-23 HH-24
31 177 0.001-0.1 20 24 0.003-0.1 20 64 0.003-0.1 32 1132 0.002-0.35 33 50 0.01-0.1 34 433 0.01-0.11 24 669 0.001-0.30 25 250 0.006-0.12 25 252 0.004-0.11 25 255 0.005-0.12 25 251 0.003-0.12 25 252 0.003-0.11 25 254 0.005-0.10 25 251 0.004-0.12 35 450 0.008-0.12 35 437 0.007-0.12 42 600 0.001-0.30 26 150 0.010-0.3 36 225 0.01-1.0
Sable silt loam HA Whitray Fell HA Whitray Beck HA Purified Peat HA Leonardite HA Eliot silt loam HA Kranichsee HA Higashiyama L HA Kinshozan P HA Kinshozan F HA Kinshozan OH HA Shitara Black HA Purified Aldrich HA Tongbersven Forest HA Vejen Landfill L1 HA Vejen Landfill L2 HA Tongbersven Forest HA PUHA Aldrich HA
145 101 42 84
i range 0.01-1.0 0.01-1.0 0.002-0.1 0.001-0.1
0.001-0.10 0.02-0.20 0.02-0.20 0.006-0.12 0.005-0.12 0.005-0.12 0.005-0.12 0.003-0.10 0.001-0.30 0.004-0.12 0.009-0.10 0.011-0.3 0.005-0.1
pH range
acquisition of data
fulvic acids 2.5-10.6 digitized from Figure 4.3 2.6-10.3 digitized from Figure 4.4 2.8-7.8 tabulated in thesis 3.1-7.2 digitized from Figure 1 as R. Convert by 4.65 mol kg-1 titratable. 3.0-10.0 reconstructed from Figure 7, using parameters given 3.2-10.8 digitized from Figure 4. Omit first point 3.5-10.0 digitized from Figure 8. Discard pH 7 or 8. The second distribution of sites was not defined by the data, and so, Qmax2,H, log K ˜ H2, and m2 could not be fitted. VOL. 35, NO. 10, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. Variation of the net negative charge of a variety of fulvic (n ) 11) and humic (n ) 15) substances versus the proton concentration in solution. The charge curves are for a range of ionic strengths. Even for datasets which did include data to pH 10, the model predicts the existence of titratable sites outside the observable pH window and therefore the experimental data still do not completely define the site distributions. For a few datasets, more usually fulvic acids, the titration curve at high pH is so flat that the fitting suggested unrealistic numbers of sites at very high log K values. In these cases, additional constraints on the second distribution were necessary. In each of these cases the values used to constrain parameters during fitting were taken from the generic descriptions derived and discussed in detail in the next section. Here their purpose was to allow the model to be fitted sensibly to datasets even when full optimization was not possible. For example, by defining a generic second distribution for a dataset with limited pH coverage, it was possible to obtain a fitted description of the first distribution and hence hopefully draw meaningful conclusions about the number and nature of binding sites in the pH range which was measured. Datasets which were fitted with constrained parameter values were excluded from the statistical summaries given in Table 2 and hence did not produce a circular analysis. All the datasets could be fitted with the model extremely well with the single exception of HH-02, where the model did not converge to a physically reasonable set of parameters. Inspection of the data for HH-02 (see Figure 2) shows that the charging curve reported is inconsistent with all of the other data available, and it is therefore reasonable to reject these dataset. The least successful fit (coefficient of determination, R2 ) 0.955) was obtained with dataset HH-01, which had already been identified as having a poor separation between data at different ionic strengths (data for 0.2 and 2.0 M almost overlie each other). As the model expects an ionic strength dependence, it was less able to explain these data well. Excluding these datasets, all the fits gave R2 of 0.98 or better. Figure 4 illustrates the range of fits by using the worst and one of the best fits for both fulvic and humic acids. The ‘worst’ fits shown were selected by taking the lowest values of R2 for datasets covering the full range of pH 3-10, after excluding HH-01 and HH-02 (discussed above). The ‘best’ fits have high R2 and were chosen as illustrating the typical fulvic and humic characteristics but avoiding the data used during original model development. It is clear that even in the worst cases, the model description is good. The results shown in Table 2 which, except where shown to be constrained, are based purely on fitting with no a priori distinction between fulvic and humic acids. They provide convincing evidence of differences in the properties of FAs and HAs. Inevitably there are some examples which do not fit the typical behavior. However, the pattern is strong (Figure 2054
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3) and is a compelling argument that humic and fulvic acids should be considered separately. Tipping (38) identified similar patterns of behavior in the Model V/VI descriptions of proton binding. The sets of mean parameter values at the foot of Table 2 provide a succinct summary of the differences. It can be seen that, in general: fulvic acids have a higher total charge than humic acids (mean 8.0 equiv kg-1 compared with 5.9 equiv kg-1); in fulvic acids a larger proportion of the sites (mean ratio 70:30) is associated with the low-pH, lowaffinity distribution than is the case for humic acids (56:44); on average, for fulvic acids the sites in the low-affinity distribution are stronger acids than for humic acids (mean log K ˜ H1 ) 2.65 compared to 3.09) while those in the highaffinity distribution are weaker acids than for humic acids (mean log K ˜ H1 ) 8.60 compared to 7.98); fulvic acids exhibit a larger Donnan volume (mean b ) 0.63 compared to 0.51), consistent with a smaller, higher charge-density particle. In broad qualitative terms, the two distributions used in the NICA model can be considered to represent the carboxylic-type and phenolic-type binding sites, respectively. These observations therefore are consistent with fulvic acids containing a larger number of carboxylic-type sites and relatively few phenolic-type sites compared with humic acids. The principal differences from the description given by Model V/VI are in the relative sizes of the two distributions (67:33 by definition for both FA and HA in Model VI) and in the width (sharpness) of the distributions. Model VI suggests that the second distribution (“type B” groups) is narrower for HA than for FA, whereas NICA-Donnan describes a broader, more heterogeneous distribution. As a consequence, the NICA-Donnan model predicts a somewhat flatter, more uniform titration curve for humic acids than that given by Model VI (38). These differences, however, are subtle. More striking is the strong overall qualitative agreement between the two model descriptions.
Derivation of Generic Parameters It would be possible to use the mean parameter values from the individual fits to describe the proton binding behavior of a new humic material about which no other details were known. However, the interdependence of the parameters in the NICA-Donnan model is nonlinear, and so simple mean values of parameters do not necessarily represent the best description of the whole data collection. A better approach is to optimize the model fit to all the datasets simultaneously. When fitting multiple datasets in this way, care has to be taken to weight the data correctly to avoid inherent weighting of the final parameter values in favor of the numerically largest, but not necessarily qualitatively best, datasets. Much of the error in the generic fit is associated with the variability between different humic substances rather than the measurement errors alone. The actual measurement errors were not available for most of the datasets. Therefore, in this work all data points were given a weighting equal to the reciprocal of the number of points in the dataset in question. Thus, the aggregate weighting of each dataset was exactly one and each dataset contributed equally to the overall fit. Single direct fits to two combined datasets, one each for fulvic and humic acids, with all parameters free to float were unsuccessful. The spread of the data points at high pH was too large and noisy to allow the identification of a unique underlying site distribution. An alternative approach to obtaining generic parameters is to fit the datasets to single descriptions of the shape of the distributions (log K ˜ H, m) while allowing each dataset to retain its own total site density, Qmax. Using this method, the number of degrees of freedom in the optimization is reduced. A specially adapted version of the fitting algorithm was developed, which allowed up to 16 datasets to be fitted with
TABLE 2. Optimal Parameter Values for the Proton Binding Data for the NICA-Donnan Model Fitted to Each Dataset Individuallya dataset
material
RMSE
R2
Qmax1,H
b
logK˜ H1
m1
Qmax2,H
logK˜ H2
m2
Qtot
Q1 %
Q2 %
FH-01 FH-02 FH-03 FH-04 FH-05 FH-06 FH-07 FH-08 FH-09 FH-10 FH-11 FH-12 FH-13 FH-14 FH-15 FH-16 FH-17 FH-18 FH-19 FH-20 FH-21 FH-22 FH-23 FH-24 FH-25
Lake Drummond FA Lake Drummond FA Suwannee River FA Bersbo FA Gota River FA Satilla River HS Gota River FA-1 Lochard Forest HA Lake Drummond FA Whitray Beck FA Suwannee River FA Armadale podzol FA Gota River FA Laurentian Soil FA Suwannee River FA Tuse FA Skagen FA Vejen Landfill L1 FA Vejen Landfill L2 FA Derwent FA Kranichsee FA Laurentian Soil FA Laurentian Soil FA PUFA Strichen FA
0.0815 0.0975 0.1529 0.0594 0.0734 0.0417 0.0159 0.0863 0.1507 0.0879 0.1236 0.1312 0.1177 0.1116 0.0738 0.0610 0.0505 0.0604 0.0570 0.0690 0.1083 0.0228 0.0692 0.0785 0.0522
0.9970 0.9946 0.9818 0.9942 0.9977 0.9987 0.9997 0.9899 0.9802 0.9966 0.9895 0.9888 0.9814 0.9936 0.9947 0.9980 0.9981 0.9977 0.9974 0.9979 0.9929 0.9996 0.9983 0.9968 0.9982
fulvic acids 0.59 6.17 0.64 5.64 0.94 4.72 0.63 5.29 0.72 5.79 0.57 5.15 0.57 3.83 0.52 7.34 0.42 5.02 0.48 5.92 0.87 5.55 0.73 5.96 0.73 5.85 0.52 8.76 0.77 5.36 0.65 6.66 0.73 5.96 0.71 6.59 0.70 6.32 0.74 6.20 0.29 5.34 0.70 3.12 0.32 2.64 0.49 6.57 0.66 5.67
2.18 2.28 3.24 3.10 2.89 2.35 2.46 2.61 2.00 2.20 3.01 3.26 2.79 2.41 3.06 2.40 2.80 2.64 2.49 2.68 2.00 3.81 2.43 2.37 2.77
0.34 0.39 0.38 0.31 0.45 0.32 0.45 0.28 0.41 0.30 0.42 0.36 0.40 0.27 0.43 0.42 0.55 0.48 0.49 0.38 0.34 0.48 0.65 0.39 0.45
1.96 2.62 1.86 1.86 0.55 1.46 2.21 1.86 0.94 0.92 1.86 1.86 1.86 1.86 3.08 1.74 1.93 6.55 2.35 2.12 5.05 1.60 7.77 1.94 1.53
8.60 9.43 8.60 8.60 8.15 8.56 9.18 8.60 7.19 7.19 8.60 8.60 8.60 8.60 8.60 8.37 8.64 10.91 9.26 9.10 9.45 7.63 7.30 8.60 8.60
0.62 0.45 0.53 0.53 0.85 0.67 0.32 0.53 0.90 0.96 0.53 0.53 0.53 0.53 0.58 0.69 0.60 0.36 0.41 0.45 0.41 0.71 0.17 0.53 0.53
8.13 8.25 6.58 7.15 6.34 6.61 6.04 9.20 5.96 6.84 7.41 7.82 7.71 10.62 8.43 8.40 7.89 13.14 8.67 8.33 10.38 4.73 10.40 8.51 7.20
75.9 68.3 71.7 74.0 91.3 77.9 63.4 79.8 84.3 86.6 74.9 76.2 75.9 82.5 63.5 79.3 75.5 50.2 72.9 74.5 51.4 66.1 25.3 77.2 78.7
24.1 31.7 28.3 26.0 8.7 22.1 36.6 20.2 15.7 13.4 25.1 23.8 24.1 17.5 36.5 20.7 24.5 49.8 27.1 25.5 48.6 33.9 74.7 22.8 21.3
HH-01 HH-02 HH-03 HH-04 HH-05 HH-06 HH-07 HH-08 HH-09 HH-10 HH-11 HH-12 HH-13 HH-14 HH-15 HH-16 HH-17 HH-18 HH-19 HH-20 HH-21 HH-22 HH-23 HH-24
Peat soil humic acid Urrbrae loam HA no 11 Leonardite HA Mosedale Beck HA van Dijk HA Sable silt loam HA Whitray Fell HA Whitray Beck HA PPHA Leonardite HA Eliot silt loam HA Kranichsee HA Higashiyama L HA Kinshozan P HA Kinshozan F HA Kinshozan OH HA Shitara Black HA purified Aldrich HA Tongbersven Forest HA Vejen Landfill L1 HA Vejen Landfill L2 HA Tongbersven Forest HA PUHA Aldrich HA
0.1748 No fit 0.1177 0.0858 0.0843 0.0464 0.0687 0.0254 0.0219 0.0262 0.1112 0.1012 0.0161 0.0278 0.0426 0.0202 0.0264 0.0120 0.0196 0.0905 0.0807 0.0540 0.0442 0.0811
0.9547
humic acids 0.49 2.99 3.15
0.51
2.55
8.00
0.26
5.54
54.0
46.0
0.9912 0.9847 0.9929 0.9987 0.9890 0.9994 0.9994 0.9993 0.9926 0.9935 0.9997 0.9995 0.9985 0.9994 0.9997 0.9999 0.9995 0.9940 0.9956 0.9953 0.9982 0.9957
0.43 0.38 0.39 0.35 0.36 0.56 0.34 0.68 0.21 0.30 0.62 0.72 0.65 0.76 0.70 0.69 0.68 0.67 0.84 0.31 0.32 0.25
3.54 2.83 2.80 2.67 3.20 3.19 2.89 3.22 2.31 1.99 3.36 3.38 2.95 3.89 3.44 3.76 3.85 2.74 3.90 2.49 2.77 2.87
0.78 0.56 0.64 0.48 0.86 0.52 0.54 0.52 0.44 0.43 0.65 0.42 0.38 0.54 0.49 0.55 0.47 0.42 0.52 0.49 0.57 0.89
2.55 2.55 3.36 0.76 3.62 2.33 4.25 3.30 1.95 3.42 3.27 0.92 1.97 0.88 1.23 2.40 1.06 5.39 3.23 2.39 2.80 5.34
8.00 8.00 8.00 6.06 8.00 7.97 8.81 8.00 7.20 8.00 8.75 7.75 8.00 8.02 7.57 8.07 8.14 10.06 8.30 8.00 7.07 8.00
0.26 0.26 0.26 0.86 0.26 0.38 0.25 0.52 0.53 0.26 0.20 0.59 0.26 0.51 0.50 0.24 0.57 0.23 0.58 0.26 0.22 0.14
6.39 5.17 6.20 5.17 5.56 5.49 6.58 7.77 6.20 6.93 5.60 5.50 5.65 3.45 5.96 5.34 3.74 9.15 5.17 4.78 5.35 7.66
60.1 50.7 45.8 85.2 34.8 57.5 35.4 57.6 68.6 50.6 41.5 83.3 65.1 74.6 79.4 55.1 71.7 41.1 37.6 50.1 47.7 30.2
39.9 49.3 54.2 14.8 65.2 42.5 64.6 42.4 31.4 49.4 58.5 16.7 34.9 25.4 20.6 44.9 28.3 58.9 62.4 49.9 52.3 69.8
3.84 2.62 2.84 4.40 1.93 3.16 2.33 4.47 4.25 3.50 2.32 4.58 3.68 2.57 4.73 2.94 2.68 3.76 1.95 2.40 2.55 2.31 summary
n min max st dev mean
25 0.0159 0.1529 0.0359 0.0814
25 0.9802 0.9997 0.0058 0.9941
fulvic acids 23 25 0.29 2.64 0.94 8.76 0.16 1.25 0.63 5.66
25 2.00 3.81 0.43 2.65
25 0.27 0.65 0.09 0.41
18 0.55 7.77 1.94 2.57
14 7.19 10.91 1.06 8.60
17 0.17 0.96 0.21 0.57
18 4.73 13.14 1.95 8.01
18 25.3 91.3 15.6 70.1
18 8.7 74.7 15.6 29.9
n min max st dev mean
23 0.0120 0.1748 0.0416 0.0600
23 0.9547 0.9999 0.0096 0.9944
humic acids 22 23 0.21 1.93 0.84 4.73 0.19 0.89 0.51 3.17
23 1.99 3.90 0.51 3.09
23 0.38 0.89 0.13 0.55
20 0.76 5.39 1.37 2.66
13 6.06 10.06 0.96 7.98
15 0.14 0.86 0.21 0.43
20 3.45 9.15 1.32 5.86
20 30.2 85.2 17.1 55.6
20 14.8 69.8 17.1 44.4
a Figures in italics show constrained parameters which were not optimized (for full explanations see main text). These values are not included in the statistical summaries. RMSE is the root mean square error in the final fit; R2 is the coefficient of determination. Q values have units of equiv kg-1.
individual values for Qmax1,H and Qmax2,H. A maximum of 16 datasets was sufficient to allow all the full-range datasets to be included for both fulvic and humic acids. Datasets with
a short pH range, or for which the individual fits had already been shown to have poorly defined second distributions, were not included at this stage. VOL. 35, NO. 10, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 4. Individual NICA-Donnan model fits to representative datasets, showing the worst (top) and one of the best (bottom) model fits to the data for each of fulvic (left) and humic (right) acids. Symbols show observed data; continuous lines show the model fits.
FIGURE 5. NICA-Donnan model fits to representative datasets using a semigeneric description with individual maximum site densities. Fits shown are for the same datasets as in Figure 4. Symbols show observed data; continuous lines show the model fits. This approach was successful. Data fitted a semigeneric distribution model very well for both the fulvic acids (11 datasets) and the humic acids (15 datasets). The quality of fits is illustrated in Figure 5, using the same datasets as are shown with free individual fits in Figure 4. The pairs of individual values for Qmax for the datasets are shown in Table 3. The single generic values obtained for the other parameters are indicated in Table 4. For both the fulvic and humic cases, the relative uncertainty of the parameter values, estimated by the sensitivity of the fit to changes in the parameters, was small. On the basis of this result, the values of b, log K ˜ H, m1, log K ˜ H2, and m2 were then fixed and the entire set of data refitted, with a single pair of free Qmax1,H and Qmax2,H values, to give the final parameter estimates shown in Table 4. These values represent the best single descriptions of the accumulated literature data that can be achieved with the NICA-Donnan model. As such, they can be recommended as the best generic 2056
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values to use for modeling proton binding with the NICADonnan model when no specific information is known about the humic material of interest. A simple sensitivity analysis showed that the final parameter values obtained in this way are relatively insensitive to the inclusion or exclusion of any individual dataset and are therefore not disproportionately influenced by particular experiments. The values are entirely consistent with the physical description of fulvic and humic acids discussed earlier. The values for the Donnan volume b parameter (0.57 and 0.49 for FA and HA, respectively) are also in reasonable agreement with those obtained by Benedetti et al. (12) using a graphical method (0.67 and 0.43). Figure 6 shows simulated titration curves derived from the generic parameter estimates for both fulvic and humic acids. These generic curves reflect the features of the majority of experimental data (Figures 1 and 2) extremely well in terms of both shape and scale, confirming that the generic
TABLE 3. Maximum Site Densities for Each Dataset, Obtained by Simultaneous Fitting to Single Semigeneric Descriptions of the Distribution Shapes (log K˜ H, m)a Qmax2,H
Qtot
Q1%
Q2%
fulvic acids 6.19 5.79
1.84 1.21
8.03 7.00
77 83
23 17
5.77
1.05
6.82
85
15
5.07 5.54
1.92 3.57
6.99 9.11
73 61
27 39
6.86 6.27 6.92 6.73 6.31
1.78 1.68 1.35 0.99 1.85
8.64 7.95 8.27 7.72 8.16
79 79 84 87 77
21 21 16 13 23
6.48
2.39
8.87
73
27
3.72
3.55
7.27
51
49
2.87 2.03
3.03 3.54
5.90 5.57
49 36
51 64
3.71 3.72 2.59 4.36 3.84 2.25 4.55 2.88 2.08
3.05 2.43 2.43 1.67 1.73 1.86 2.15 2.92 2.49
6.76 6.15 5.02 6.03 5.57 4.11 6.70 5.80 4.57
55 61 52 72 69 55 68 50 46
45 39 48 28 31 45 32 50 54
2.30 2.70 3.30
2.28 3.07 3.04
4.58 5.77 6.34
50 47 52
50 53 48
n min max st dev mean
fulvic acids 11 5.07 6.92 0.58 6.18
11 0.99 3.57 0.73 1.78
11 6.82 9.11 0.77 7.96
11 60.8 87.2 7.3 77.9
11 12.8 39.2 7.3 22.1
n min max st dev mean
humic acids 15 2.03 4.55 0.82 3.13
15 1.67 3.55 0.61 2.62
15 4.11 7.27 0.88 5.74
15 36.4 72.3 9.7 54.1
15 27.7 63.6 9.7 45.9
dataset
material
FH-01 FH-02 FH-03 FH-04 FH-05 FH-06 FH-07 FH-08 FH-09 FH-10 FH-11 FH-12 FH-13 FH-14 FH-15 FH-16 FH-17 FH-18 FH-19 FH-20 FH-21 FH-22 FH-23 FH-24 FH-25
Lake Drummond FA Lake Drummond FA Suwannee River FA Bersbo FA Gota River FA Satilla River HS Gota River FA-1 Lochard Forest HA Lake Drummond FA Whitray Beck FA Suwannee River FA Armadale podzol Bh FA Gota River FA Laurentian Soil FA Suwannee River FA Tuse FA Skagen FA Vejen Landfill L1 FA Vejen Landfill L2 FA Derwent FA Kranichsee FA Laurentian Soil FA Laurentian Soil FA PUFA Strichen FA
HH-01 HH-02 HH-03 HH-04 HH-05 HH-06 HH-07 HH-08 HH-09 HH-10 HH-11 HH-12 HH-13 HH-14 HH-15 HH-16 HH-17 HH-18 HH-19 HH-20 HH-21 HH-22 HH-23 HH-24
Peat soil humic acid Urrbrae loam humic no 11 Leonardite HA Mosedale Beck HA van Dijk HA Sable silt loam HA Whitray Fell HA Whitray Beck HA PPHA Leonardite HA Eliot silt loam HA Kranichsee HA Higashiyama L HA Kinshozan P HA Kinshozan F HA Kinshozan OH HA Shitara Black HA purified Aldrich HA Tongbersven Forest HA Vejen Landfill L1 HA Vejen Landfill L2 HA Tongbersven Forest HA PUHA Aldrich HA
Qmax1,H
humic acids
summary
a
The best fit values for the other parameters are shown in Table 4. Q values have units of equiv kg-1.
parameters provide a realistic representation of the observed behavior of typical humic materials. Figure 7 shows the intrinsic proton-affinity distributions associated with these descriptions. Although the model necessarily generates
continuous distributions, the forms of the curves are still instructive. For the humic acids, the distribution of sites is very broad, implying a large degree of heterogeneity, leading to relatively flat, constant-gradient titration curves. For the VOL. 35, NO. 10, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 4. Optimal NICA-Donnan Parameter Values for Generic Fits to All Available Proton Binding Data for Fulvic and Humic Acids Using (i) Single Semigeneric Site Distributions with Individually Adjustable Maximum Site Densities for Each Material and (ii) Single Universal Descriptions Applied to All Materialsa RMSE
R2
b
individual site densities single generic site density
0.123 0.591
0.992 0.805
0.57
individual site densities single generic site density
0.127 0.631
0.989 0.719
0.49
Qmax1,H
logK˜ H1
fulvic acids 6.18 2.34 5.88 humic acids 3.13 2.93 3.15
m1
Qmax2,H
logK˜ H2
m2
Qtot
Q1 %
Q2 %
0.38
1.78 1.86
8.60
0.53
7.96 7.74
77.9 76.0
22.1 24.0
0.50
2.62 2.55
8.00
0.26
5.74 5.70
54.1 55.3
45.9 44.7
a The Q values shown in italics for the case of adjustable semigeneric distributions are mean values. Values in bold are the recommended generic values. All Q values have units of equiv kg-1.
Importantly the model continues to predict, as the data suggest, the existence of titratable sites with affinities well outside the normal experimental range. Figure 6 shows that only 55-60% of fulvic and 65-70% of humic sites can be titrated in the experimental window between pH 3.5 and 10.5. However, these ‘unseen’ protons are of potential importance in metal-ion binding since strongly bound metal ions such as Cu2+ may displace them. A simple alternative procedure to estimate the number of available sites for use in the NICA-Donnan model would therefore be to perform a single titration from pH 3.5 to 10.5 and then multiply the result by a factor of 1.5. These sites can be assigned to either Qmax1,H or Qmax2,H according to the proportions derived from the generic fits (0.76 and 0.55 for Qmax1,H for FA and HA, respectively, see Table 4) More generally, if titration data are available for a narrower range of pH, then the Qmax,H can be estimated by comparing the observed change in charge, ∆Q, over any given pH interval with that expected from the generic FA or HA fit and scaling the generic figures for Qmax,H accordingly. The expected ∆Q for the generic fit for a fixed ionic strength of 0.1 M can be quickly but reliably obtained from FIGURE 6. Simulated titration curves for proton binding by fulvic and humic acids corresponding to the generic NICA descriptions given in Table 3. Four concentrations of background electrolyte (from bottom to top, 0.003, 0.01, 0.03, and 0.1 M) are shown over the ‘full’ pH range from 0 to 14. The true ionic strengths inevitably vary, particularly at the extreme pH values where the proton or hydroxyl concentrations dominate. The dashed vertical lines represent the limits of the normally practicable experimental range, so the curves between these limits are what might be observed in the laboratory.
FIGURE 7. Intrinsic proton-affinity distributions associated with the generic NICA descriptions for proton binding by fulvic and humic acids. fulvic acids, the steeper unequal distributions generate a titration curve with marked “hips” or changes of gradient at the peaks of the distributions and a clear inflection at around pH 8 (the minimum at log KH ) 6.5 in Figure 6) as the titration moves from the large low-affinity distribution to the smaller high-affinity distribution. 2058
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[
Γ ) R1 1 -
(β1H)γ1 1 + (β1H)γ1
] [
+ R2 1 -
(β2H)γ2
]
1 + (β2H)γ2
(3)
where H ) proton activity ()10-pH), Γ ) -Q (mol kg-1), and for fulvic acids R1 ) 5.74, β1 ) 5.30 × 103, γ1 ) 0.36, R2 ) 2.01, β2 ) 1.61 × 1010, γ2 ) 0.45 while for humic acids R1 ) 2.51, β1 ) 1.39 × 104, γ1 ) 0.46, R2 ) 3.33, β2 ) 1.00 × 109, and γ2 ) 0.19. Note that eq 3 has the form of a double-distribution Langmuir-Freundlich isotherm but unlike the NICA-Donnan model isotherm can be calculated explicitly without iteration. Substituting two pH values in turn gives ∆Γ ()-∆Q) for a generic FA or HA, which by comparison with the corresponding Qtot from Table 4 gives a scaling factor to use for the sample material. Qtot for the sample can be divided between the two distributions according to the percentages given in Table 4. Three progressively more generalized stages of modeling proton binding with the NICA-Donnan model are thus possible: (1) If detailed acid-base proton titration curves are available, the model should reproduce the data over the full experimental range, typically with R2 ) 0.996 or better and RMSE of the order of 0.08 equiv kg-1 or better (approximately (0.16 equiv kg-1 at 95% confidence level). (2) If a single titration or measurement of the total site density is available, the model can use the assumption of semigeneric site distributions to predict binding behavior with an RMSE of 0.12 equiv kg-1 (approximately (0.24 equiv kg-1 at the 95% probability level). (3) If no knowledge of binding behavior or site density is available for a specific material, the model can be expected to predict proton binding for a FA or HA to within an RMSE of approximately (0.5 equiv kg-1 over the pH range 3-11, i.e., 10-15% of the total titratable charge.
Calculations using the NICA-Donnan model are necessarily iterative and therefore not trivial (although they can be done in a spreadsheet). To be more generally useful, the NICA-Donnan model needs to be incorporated into the popular general-purpose geochemical speciation programs, such as PHREEQC, so that it can be readily combined with other geochemical models
Further Information The full published datasets used in this work are available on the BGS website at www.bgs.ac.uk/humics. We would welcome any notification of additional datasets for inclusion in the database.
Acknowledgments We are grateful to Marcelo Avena, Marc Benedetti, Jette Christensen, Iso Christl, Martin Glaus, and Sandy Robertson for providing original experimental data, in some cases before formal publication of their own work. We thank Willem van Riemsdijk for discussion and encouragement, and we appreciated a helpful, but anonymous, review. The work was funded by the Natural Environment Research Council (Grant No. GR9/3481) and the European Commission Framework IV Program (Grant No. ENV4-CT97-0554). C.J.M. and D.G.K. publish with the permission of the Director of the British Geological Survey.
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Received for review June 13, 2000. Revised manuscript received December 18, 2000. Accepted January 5, 2001. ES000123J
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