Environ. Sei. Techno/. 1995, 29, 446-457
8
8
Metal Ion &IltkRg to Humic Substances: Awwtion of the
MARC F. BENEDETTI,",t,t CHRIS J . M I L N E , § D A V I D G . KINNIBURGH,S WILLEM H. VAN RIEMSDIJK,*tt A N D LUUK K . K O O P A L " Department of Soil Science and Plant Nutrition and Department of Physical and Colloid Chemistry, Wageningen Agricultural University, Dreijenplein 10, 6703 HB Wageningen, The Netherlands, and British Geological Survey, Wallingford, Oxon, OX10 8BB, U.K.
The application of a new model to describe metal ion binding by humic acids is discussed. Metal ion binding is always of a competitive nature since the proton is always present. Although of great practical importance, the combination of a chemically heterogeneous system with competitive binding poses difficult problems from both experimental and theoretical points of view. The new Non-Ideal Competitive Adsorption model (NICA model) used here is able to account for the non-ideal binding to heterogeneous ligands. A good description of the binding of H, Ca, Cd, and Cu to a purified peat humic acid is achieved over a wide range of free metal ion concentrations (-2 7 log Me2+ 7 -14) and pH (2 < pH < 10). The results show that binding of metal ions to humic acid is strongly influenced by the intrinsic chemical heterogeneity of the humic material itself as well as by ion-specific non-ideality. The results indicate that copper competes much more efficientlywith protons bound to the phenolic type groups than calcium and cadmium.
Introduction Humic substances play an important role in the behavior and fate of metal ions in the natural environment. They can control metal ion concentrations in soils and natural waters and can affect the mobility of metals through soils and aquifers (I, 2). The interaction between metal ions and soil particles can also be controlled by humic substances. Humic substances are believed to play a major role in trace metal availability and toxicity to plants and living organisms. Among the humic substances, the humic acids (HA) and fulvic acids (FA) are polydisperse mixtures of natural organic polyelectrolytes having different types of functional groups to which ions can bind. Two major types of functional groups are of particular importance: carboxylic groups and phenolic groups (3-7). Amino, sulfhydryl, and quinone groups can also be present and may have strong interactions with trace metal ions (1,3,4). However, since their number is much smaller, their contribution to ion binding is also generally small, although under certain conditions it can be substantial. In natural systems, metal ion binding will be affected by different processes and humic acidproperties. Due to their diverse functional groups, the humic acids behave as heterogeneous ligands (1,4-9), and this chemical heterogeneity will be reflected in their ion binding properties. The polyelectrolytic behavior of humic acids will also affect ion binding due to electrostatic interactions (1,5,6,9- 12). Natural waters contain a variety of ions that will compete to a greater or a lesser extent for the available binding sites. Protons are always present in aquatic systems, and they too will compete with metal ions for binding to humic acids. The proton concentration determines the degree of ionization of the functional groups as well as the charge of the humic acids. Multivalent ions such as Ca2+,Mg2+,Fe3+, andA13+are known to bind to humic acids ( 1 ) . In principle, all these ions will compete for the same sites and hence influence the binding of each other. The complexity of such a system is great and has led to the development ofvarious models (2,10,11,13-15).The aim of forward modeling is to be able to describe ion binding at different pH's and ionic strengths and over a wide range of concentrations for the different ions. Models of ion binding by humic substances described in the literature can be divided into two categories: those assuming a discrete distribution of ligands and those assuming a continuous distribution of heterogeneous ligands. The discrete ligand approach can successfully describe metal binding in the absence of competing ions (proton excluded) within the range of the conditions of the calibrating titrations (13). Although competition among ions can be described by the discrete approach, because of the variable nature of the natural ligands discrete models generally require extra * Corresponding authors; e-mail address: Willem van
[email protected];Fax: 31 83 708 37 66. t
Department of Soil Science and Plant Nutrition.
* On leave from GCosciences de I'Environnement Ura CNRS 132, Case 431, FacultC des Sciences de St Jkrdme, 13397 Marseille Cedex 20, France. 5 British Geological Survey. '1 Department of Physical and Colloid Chemistry.
446 8 ENVIRONMENTAL SCIENCE &TECHNOLOGY / VOL. 29, NO. 2.1995
0013-936X/95/0929-044&$09.00/0
0 1995 American Chemical Society
ligand sites in order to satisfactorily match the experimental data (16). Whether this difficulty can be overcome by models based on a continuous distribution is still a matter of discussion (15). Dobbs et al. (171 and Susetyo et al. (14) successfullyused a continuous binding site model to predict the effect of protons and Al on Eu binding to humics. Up until recently, the main restriction with models based on a continuous distribution is that it is assumed that the different metal ions experience the same chemical heterogeneity (15, 18). When single metal ion adsorption experiments are carried out using the same humic acid, it is found however that the different metal ions do not experience the same apparent heterogeneity. Competitive adsorption cannot then be adequately described by the “classical” (18) multicomponent models. Therefore, to address this problem, Koopal et al. (19) developed a new non-ideal competitive adsorption (NICA) model in which heterogeneity and component-specific non-ideality are considered explicitly. The NICA model is based on a continuous distribution of heterogeneous ligands in which the overall non-ideality is divided into an intrinsic heterogeneity contribution (a property of the humic substance) and ion-specific nonideality contributions. In the NICA model, the polyelectrolytic nature of ion adsorption to humic substances is accounted for in a generic way by the non-ideality parameters. In literature, several attempts have been made to model the electrostatic interactions more specifically. For example, Tipping and Hurley (15) use an empirical equation to relate charge and potential. Marinsky et al. (10,20,21) employ a Donnan potential term, and De Wit et al. (5, 6, 9), Bartschat et al. (12) and Milne et al. (22) compute the electrostatic potential with the PoissonBoltzmann equation, assuming a given geometry (e.g., sphere or cylinder) for the shape of the FA or HA particles. It is also possible to extend the NICA model to take into account specificallythe ionic strength effectson both proton and trace metal binding, and we will return to this aspect in a future paper. The binding will be studied predominantly at a single ionic strength of 0.1 M. We assume that at constant ionic strength electrostatic interactions are of similar magnitude for the various divalent ions under investigation. The aim of this paper is to test the NICA model for a wide range of competitive conditions using a single humic acid sample. The sample used is a purified peat humic acid (PPHA) for which the proton-charging behavior has previously been analyzed using an electrostatic diffuse double layer model ( 7 ) . Ca and Cd (22) binding data are also available for the PPHA material, and new experimental data for Cu binding are presented here. Hence, the model can be tested with H, Cd, Cu,and Ca data for the same humic acid. In the following, we will first briefly describe the experimental procedures adopted and then describe the model and its use for modeling proton and trace metal binding.
Experimental Section All experiments were performed on purified peat humic acid (PPHA),the purification and properties of which have been described by Milne et al. (7). The initial concentration of the humic acid suspension was 5.28 mg of PPHAlg of suspension. Potentiometric experiments were carried out using a fully automated titration system, which is described in detail elsewhere (23).
z
2oo 150 I00
Y
E
t
-
-
500 -50
Regression fit:
E,,= 307.7f 1.6 mV SI = 30.9f 0.1
-
-1001 I I -13 -12 -11 -IO
I
-9
I
-a -7 log (CU*+)
I
-6
-5
I
-4
-3
I
-2
FIGURE 1. Calibration curve for Cu ISE produced by titrating Cuwith ethylenediamine. Free Cu activities were calculated explicitly for each point using a speciation model,the measured pH, and the total concentrations of the components. Two Q limits are shown.
Cadmium and Calcium. Data for Cd and Ca binding to PPHA are taken from Milne et al. (22). Metal ion concentrations were measured potentiometricallyusing Cd or Ca ion-selective electrodes (ISE) to give ion binding isotherms at pH 4,6, and 8 for Cd and at pH 6, 8, and 10 for Ca. All experiments were performed in a 0.1 M KN03 background electrolyte. Copper. Copper concentrations in solution were measured potentiometrically using a sulfide-based solid-state ion-selective electrode (Orion 9429). This technique has been used before for measuring Cu binding to humic materials with considerable success (24, 25). It was demonstrated using ethylenediamine (en) titrations that linear response of Cu ISEs can be obtained for Cu activities as low as pCu 19 (26). Other authors have calibrated using standard solutions at higher Cu activities and have assumed an extension of the calibration using linear (24) or polynomial extrapolation (25). Here the electrode performance was verified by titrating aqueous (en) (0.1 M) into Cu(N03)z (0.01 M). The total concentrations of the component species and the measured pH were then fed into the ECOSAT speciation model (27) to calculate the concentration and activity of free Cu2+at each point in the titration. Stability constants for complexes were taken from refs 28 and 29:
+ Cu2+ + 2en H + H(en)
Cu(en) f Cu2+ en Cu(en), f H2(en) f
log K = 10.48 log K = 19.55 log K = 6.848
The calculated free Cu activities were plotted against the observed ISE emfreadings to give a calibration curve (Figure 1)which was linear over the whole range of the calibration titration frompCu 2 to pCu 12. For experimentaldata points between pCu 12 and pCu 14, we assume that the linear response continues; we saw no evidence to the contrary during the experiments. The fitted slope of the calibration (30.9 mv) is larger than might have been expected from Nernstian theory, but it was consistent and reproducible both in calibrations and during experiments with humic acid. VOL. 29, NO. 2, 1995 / ENVIRONMENTAL SCIENCE &TECHNOLOGY 1447
During the calibration titration, up to 20 minwas allowed for each dose to equilibrate before a reading was taken. The full titration procedure therefore took approximately 16 h, which was too time consuming to allow satisfactory routine calibration of individual experiments. Routine calibration therefore used only unbuffered solutions to M Cu(NO3I2in 0.1 M KNOd and tookup to 2 h. Full calibrations were repeated at intervals to verify that the ISE performance continued to be linear. We saw no evidence that the performance of the Cu ISE was disturbed by the presence of the humic acid (24). This conclusion is also supported by other authors (301,who using electron microprobe analysis were unable to detect adsorption of fulvic acid on the surface of the electrode. pH stat experiments were carried out at pH 4,6, and 8. A solution of PPHA in 0.1 KNO3 was titrated to the stat pH (0.004 pH) and then maintained for up to 12 h to stabilize the PPHA before C u ( N 0 3 ) ~was added to the solution in progressivelylargerdoses. The additions were done in two ranges, high Cu (0.1 M C U ( N O ~in) ~ HzO) and low Cu in 0.1 M KN03). The concentration of free Cu was measured after the stat pH had been maintained for 15 min, and the Cu electrode deviation was less than 0.2 mV min-l. This generally meant that there was a total time of 25-35 min between successive Cu doses. The total concentration of Cu species in solution was then calculated, and the amount of bound Cu2+was estimated by difference. The H+/Me2+ exchange ratio was corrected for the hydrolysis of the unbound Cu in solution. The binding data have been corrected for Cu hydrolysis products using thermodynamic data of Baes and Mesmer (31). In solution, CuOH+ (log &"OH+ = -8) is the major hydrolysis species; higher complexes have only trace importance. The dominant hydrolysis feature is the precipitation of CU(OH)~ (log Ksp = 8.641, which precludes ISE measurements at log[Cu2+]> -3.3 for pH 6 and log[Cu2+]> -7.3 for pH 8.
where Qi,r is the total amount of component i bound to the humic acid, and Qmaxisthe total site density. is a median affinity constant for component i, and ci can be either the concentration or the activity of i. The parameter niaccounts for the "non-ideal" behavior (nf 1, non-ideal; n = 1, ideal) of component i. For ion adsorption, Izi takes values of 0 < ni 5 1. The value of p (0 < p 9 1) determines the width of the distribution due to the intrinsic chemical heterogeneity of the sorbent and is the same for all components. The value of p cannot be obtained from monocomponent binding data since in this case only the combined effect can be deduced. Therefore, a multicomponent set of binding data are needed to derive the value p for a given sorbent. The more classical (ideal behavior) multicomponent Langmuir-Freundlich eq (18)follows from eq 3 if all ni are set equal to 1:
This reaction implies monodendate binding to all of the sites. The total adsorption @,, of a component i is then described by the following integral equation:
Equation 4 gives very poor results for the description of pH-dependent metal ion binding to humic materials ifnonideality effects due to lateral electrostatic interactions or due to component-specificheterogeneity are not accounted for as has been shown for Cd binding to soil water-derived fulvic acid (data set of Saar and Weber (25))by Koopal et al. (19). Moreover, pH-dependent copper binding cannot be described in a satisfactoryway using this approach. The NICA approach has been shown to be able to give excellent results for pH-dependent cadmium binding to fulvic acid when electrostatic interactions are not accounted for explicitly (19). Experimentalevidence indicates that there are two major types of site in the affinity distribution for the binding of protons andlor metal ions to humic substances ( 4 - 7 ) , usually considered to be due to carboxylictype groups and phenolic type groups, respectively. We can now extend the NICA model to reflect this by introducing a bimodal affinity distribution which transforms eq 3 to
where fllog KJ is the distribution function of the affinity constant, Oi,l is the local adsorption isotherm, i.e., the binding to a group of identical sites (32),and Alog Ki is the range of log & to be considered. This equation can be solved analytically for certain distribution functions in combination with certain local isotherms. For a multicomponent system, Koopal et al. (19) have derived the following nonideal competitive adsorption expression for @ j , t by using the extended Henderson-Hasselbalch as the non-ideal local isotherm in combination with a LangmuirFreundlich (LF) type affinity distribution function (quasiGaussian) by Sips (33):
where the subscripts 1 and 2 relate to the first and second peak of the aflinity distribution. Figure 2 illustrates schematically the general procedure which is used to derive the various parameter values of the NICA model for a multicomponent set of ion binding data.
Model Description The proton or metal ion binding to each site type S at the ligand is assumed to follow the reaction:
448 1 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29. NO. 2, 1995
STEP 1
Charge us. p H data
INPUT PARAMETER OPTIMISATION
OUTPUT
STEP 2
NICA: eq 6 &pus
Err and m~
1 set of metal binding experimental data at different
INPUT
PARAMETER OFTIMISATION
PH NICA: eq 3 or 5
g,,ni andp (r, same for all
OUTPUT
other elements) SUBSEQUENT
I other set of metal binding experimental data at different
INPUT
METALS
PARAMETEROPTIMISATION
PH NICA: eq 3 or 5
g, andni
OUTPUT
FIGURE 2. General scheme of the fitting procedure used during modeling with the nonideal competitive adsorption model (NICA).
First, monocomponent binding data are used in order to derive a value of mi describing the combined effect for one component (mi= nip). For this purpose, the proton binding as a function of pH in indifferent electrolyte is used. The salt level is chosen to be the same as what is used for the study of the metal ion binding. A relatively high salt level may be chosen to suppress the effects due to electrostatic interaction. In the first step, the value of the average proton affinity constants, the total number of sites, and the value of mH for both peaks can be established. In the second step, the value of p can be derived using data from a metal binding experiment in which metal binding is studied as a function of the metal concentration at different pH’s. This enables p to be calculated from both the metal and the proton data and at the same time & and ni can be derived for the metal. The value of nH is given by mdp. For subsequent metal ions, only& and ni have to be derived since p is already known. Therefore, each new metal ion species requires only two new parameters for each affinity distribution. For the extended NICA (eq 5 ) , the same procedure applies, but now the constants for both groups of sites should be determined. To summarize, for the extended NICA model, six parameters are derived from the proton data. These consist of two median affinity constants, two site densities, and two W -values I corresponding to the widths of the two apparent affiinity distributions. Then for the first metal, i, six additional parameters have to be derived: again two median affiiity constants for metal i, plus two pvalues and two ni values. Finally, each additional metal requires four further parameters: two median affinity constants and two values for nj, The total number of parameters needed to describe the interaction of the proton and one metal with humic, 12; is moderately high but is within the range used by other authors, e.g., 10 parameters (34)or 13 parameters (1.9, and reflects the complex heterogeneous nature of humic materials. However, if within the range of the experimental conditions only one group of sites (e.g., the carboxylic) is needed to account for the observed experimental binding curves, the basic NICA (eq 3) can be used and only six parameters will be needed to model the binding of a proton plus one metal. The pH-dependent cadmium
binding to fulvic acid as measured by Saar and Weber (25) can be described perfectly in this way (19).
Results Experimental Data Proton. The proton data are discussed extensively elsewhere (3,but since the proton charging curve is used to derive the proton parameters the major results are summarized here. Surface charge versus pH curves for the PPHA measured at different ionic strength could be modeled reasonably well with the master curve (surface charge versus surface pH) approach (7, 9). Heterogeneityanalysis (3.536)of the data suggestedan affinity distribution with two peaks. Since the proton binding curve to PPHA at 0.1 M KN03 is used to obtain the proton parameters ( & , mH, and Qmax) for each of the two peaks of the affinity distribution, the experimental binding curve and the derived affinity distribution are shown in Figure 3, panels a and b, respectively. Metals. The symbols in Figure 4 present the Cd binding data, log[Cdad,],as a function of free cadmium concentration, log [Cd2+l,for pH 4,6,and 8. The binding is strongly pH-dependent as previously seen by Saar and Weber (25) for fulvic acids. Cadmium binding increases with increasing pH, although the separation between the pH 4 and 6 and the pH 6 and 8 curves in the log-log plot is not the same. In Figure 5, the measured Ca binding is given for pH 6, 8, and 10, by the symbols, as before; results are plotted as lOg[ca&]versus log[Ca2+l.As for Cd, the binding is strongly pH-dependent with more Ca bound to the humic acid at higher pH. . The Cu binding data (log[cuad,] versus log[Cu2+l)are shown by the symbols plotted in Figure 6. Results show similar features to the other two metals, but Cu is clearly more strongly bound than Ca or Cd. The extent of binding is comparable to that found for Cu binding to Suwannee River fulvic acid and natural DOC (34, 37). A comparison between the binding on PPHA of Cu, Cd, and Ca at pH 6 and in a 0.1 KN03background electrolyte is given in Figure 7 . The effect of pH on the binding (Figures 4-6) is larger for Cu than for Cd, and for Cd it is larger than for Ca. It should be noted that the slope of the different VOL. 29, NO. 2, 1995 / ENVIRONMENTAL SCIENCE & TECHNOLOGY 449
Delta Charge in m o m 4
I
3 t
2
4
10
8
6
PH
1
decreasing from 0.9 to 0.3 with increasing free metal concentration. A similartrend is also found for Cu, but the observed exchange ratio is always greater than 1, ranging from 1.8 to 1.3. For all three metals, pH has little effect on the observed exchange ratio. Modeling. Modeling the Proton Binding, In the first step of the determination of the model parameters, the surface charge pH data at 0.1 M ionic strength are required. However,direct measurement provides data for AQ (relative surface charge) versus pH. AQ was converted to Q by assuming an initial charge, Qo, (based on experimental determinations) of 0.35 equiv kg-1 (see discussion of Qo in Milne et al. (7)). The thus obtained data are shownin Figure 3A, and these data are fitted with the extended NICA (eq 5) model, which simplifies to eq 6 if the proton is the only cation present in the system:
B /
0.5
0
2
4
8
6
10
logK B
FIGURE 3. (A) Charge ( S O ) as a function of pH curves in e 0.1 N 1:l electrolyte. (B) Proton affinity distributionobtainedfromQvarsus pH curve for the purified peat humic acid (PPHA) at 0.1 M ionic strength (data from Milne et al., ref 22).
binding curves at low adsorption values is not the same for all three metals. Exchange Ratio. Since pH was maintained constant during the metal binding experiments, it is possible to estimate a H+/Me2+molar exchange ratio from the amount of base required to pH stat the system after each addition of metal. The observed exchange ratios are given by the symbols in Figure 8 for Cu, Cd, and Ca at pH 6 and 8. Cd and Ca have an observed exchange ratio less than 1,
Fitted parameters values are given in Table 1; fitted results are shown in Figure 3A as the drawn curve. The first peak (log = 4.60 L mol-', ml = 0.44, and Qmax,i = 2.48 mol kg-') can be assigned to carboxylicmoieties while the second peak (log KH,~ = 9.34 L mol-', m2 = 0.39, and Qmm,2 = 1.93 mol kg-l) can be assigned to more "weakly acid" groups such as phenols, alcohols, and enols (4). In this monocomponent case, the m parameter reflects the apparent heterogeneity of the humic acid, which combines the effects of intrinsic heterogeneity together with those due to non-ideality experienced by the proton. This ionspecific non-ideality includes the electrostatic interactions at a given ionic strength. The moderately small values of both ml and m2 indicate that the humic acid exhibits a strongly heterogeneous and/or non-ideal behavior withrespect to protons. From the values of Qma,it is apparent that the carboxylic type of sites are more numerous than the weak, phenolic type sites. This supports the general observation that carboxylic type groups are more abundant than the weak acid groups (38). The proton-derived values for the various parameters given in Table 1 are also assumed to apply in the presence
log{[Cd ads]/mol kg-1)
-1
I I
-10
I
-8
-6
-4
-2
log((Cd2+]/moll-1} FIGURE 4. Cadmium binding to the PPHA as a function of log[Cd*+I at pH 4,6, and 8 showing the comparison between experimental data and the NICA model description. 450
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29, NO. 2, 1995
log{ [Ca ads]/mol kg-1) 1
0
-1
-2 -6
-5
-4
-2
-3
log([Ca 2+ ]/mol I
-'1
FIGURE 5. Calcium binding to the PPHA as a function of log[Ca2+1at pH 6,8, and 10 showing the comparison between experimental data and the NlCA model description.
log{ [Cu ads]/mol kg-1)
t -4 I
1
II
-4
-2
pH: 6' I
-14
-12
I
I
I
-10 -8 -6 ~og([Cu2+]/mol1-9
FIGURE 6. Copper binding to the PPHA as a function of log[Cuz+] at pH 4, 6, end 8 showing the comparison between experimental data and the NlCA model description.
of metal. The competitive nature of the NICA model requires the assumption that Q m a x , ~= Qmax,metd. Furthermore, ml and m2 will be used to derive p l and pz in the multicomponent case (Figure 2). Modeling Ca, Cd, and Cu Data. Metal ions bound in the diffuse double layer could produce differences between model results and the experimental data. However, it is possible with a Donnan model (10,20,21) to estimate the composition of the diffuse layer and to correct for electrostatic effects. These matters will be discussed in a separate article (391,but an important conclusionfrom these calculations is that non-specific binding is always lower than 1-10% for all metals (high values occurring for high metal concentrations). A similar result has been found by Tipping and Hurley (15) . Therefore, we have decided to neglect diffusely bound metal. We have already emphasized the large number of parameters needed in the NICA model during step 2 of the
fitting procedure (Figure 2). Initial estimates of the six parameters are needed before automatic optimization can proceed. Although in numerical fitting procedure a "blind guess" could be made for the initial values for each parameter, we prefer to derive initial estimates of the metal parameters graphicallyfrom the adsorption curves. In this way, failure of convergence in the fitting routine is minimized. For the graphical analysis, the second peak in eq 5 is neglected. This simplification is the more reasonable the lower the pH. At constant low pH and low free metal ion concentration, it is assumed that the proton term in eq 3 is constant and always much larger than the metal term, i.e.
KHcH
= constant
(7a)
and VOL. 29, NO. 2, 1995 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
461
log{ [Metal ads]/mol kg-1) 11 pH=6 0-
-1
-
-2
-
-3
-
cu
*e
-*** *e** *
** *-* + oow *
$0
0-
00
** **
0 00
' Cd
00
I
-10
-12
-8
-6
-4
-2
log{ [Me 2+]/mol1") FIGURE 7. Comparison of the relative strengths of Ca, Cd, and Cu binding to PPHA at pH 6. (&CHI
nH
>> ( ~ C niJ
(7b)
Then the right-most term in eq 3 is equal to a constant, and eq 3 reduces to a Freundlich isotherm:
(8) or log Qi,, = log Qma5+ ni log (ci)
(9)
where the product Qmax5 is a constant that is dependent on the pH. In a log-log plot such as Figure 4, the limiting slope of the isotherm at constant pH corresponds to ni, which is the parameter describing the non-ideal behavior of the humic materialwith respect to the bound metal. The limiting slope of the isotherm thus provides the ni value. Note that this analysis also exposes the weakness of the classical multicomponent equation since the limiting slope of the eq 4 isotherm is always 1regardless of the nature of the element under investigation, and yet it is clear from our experimental results for Cd and Cu (Figures 4 and 6) that this is not often the case. Hence, as was previously shown by Koopal et al. (19) with literature data from Saar and Weber (2.9, eq 4 cannot adequately describe the experimental data. Equation 3 can also be reduced to another simplified form. This time the proton term is no longer assumed to be constant, but it is still assumed to be much larger than the metal term at low metal concentrations and also RHCH is assumed to be larger than 1 i.e., eq 7b still applies. This leads to (10)
and
log Qi,, = log Y
+ ni
where v is a new constant equal to Qmax@ilKHnH. The shift of the logarithm of the free metal ion concentration for a given value of bound metal as a function of a change 452 1 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29, NO. 2, 1995
in pH can be derived from eq 11 and gives:
When ni is estimated graphically as previously described, it is relatively easy to derive an estimated value for n~from the metal log-log plots at two different pH values. Once nH is estimated, an estimated value for p can be derived from mH = nHp. Estimates of p , ni,and nH were made in this way for both the Cd and Cu binding data (Figures4 and 6).
Another limiting equation for the shift of the curve of a Freundlich plot as a function of pH at constant (low) amount of metal bound and intermediate pH values has been derived by Van Riemsdijk (40) and can provide estimates of n~ and p under the conditions that (&ci)"i 10) is clearly demonstrated; less than 50% of the bound Cd is associated with the carboxylic sites under these conditions. The contribution of the phenolic sites to Cu binding is substantial over the whole pH and Cu concentration range although the carboxylic sites are more important at high concentrations of Cu (pCuz+ < 6) and low pH. Again, the contribution of the phenolic sites becomes increasingly important with increasing pH. At pH 6 and pCu2+ > 10, 70% of the bound Cu is associated with the phenolic sites while at pH 8 and pCu2+= 14 this increases to 95%. This finding suggests that the copper ion binding to humic substances in most natural surface waters is dominated by the binding to the weak acid sites since the pH is typically around 8 and the free copper ion concentration can be as low as mol L-l (46). That the phenolic sites become more significant in the metal ion
TABLE 4
pKl and p K 2 Values Derived with the NICA Model for Different Metals: Comparison with Recent Literature Values Tipping and Hurley (1s)
"4
-12
-10
-8
-6
-4
-2
20 -
010
-8
-6
-4
-2
-3
-2
6oI
40
20
pH8pA6
6
-5
-4
log[Me*+]molI-1
FIGURE 9. Contribution of the carboxylic sites to the total binding of Cd, Ca, and Cu to the PPHA at pH 6 and 8. Calculated from the NICA model by setting the contribution of the phenolic sites to zero be., L,Q = 0) and using the parameter values of the carboxylic sites given in Table 3, Section A. The x-axis range, different for each metal ion, corresponds to the range of the experiments.
binding at high pH is an expected result and is in accord with observations in literature (34,47). The more striking result of the model is that the phenolic sites still dominate at lower pH values provided that the free metal ion concentration is low. The advantage of the bimodal NICA approach is that it is capable of describing the metal ion binding over a very wide range of conditions for all cations tested. The model can be simplified considerably, without much loss of accuracy, if one is only interested in metal ion binding over a limited range of conditions. For metal ion binding at constant pH, the model can even be simplified to the two parameters of classical Freundlich equation (eq 8). For conditions where either the phenolic or the carboxylic sites dominate the binding, the pH-dependent binding can be described with a monomodal NICA model. Comparison with a Different Approach and Uniqueness of the Parameters Sets. In a recent paper, Milne et al. (22) followed a different approach to model cadmium and calcium binding to PPHA. Two different models were tested. The physically most realistic optionwas the bimodal competitive LF model in combination with a cylindrical double-layer model to account for electrostatic interaction. The binding of both cadmium and calcium could be described reasonably well assuming that they bind to the carboxylic type groups. The results were not as good as
Ca CU Cd
Milne et al. (22)
this work
pKMHA
PKMHB
PL
pki
PL
pki
1.97-3.39 0.36-1.09 1.41-1.61
6.03-8.76 3.03-5.69 5.24-5.83
0.74
0.51
2.26
3.10
2.77 1.19 1.65
7.21 1.17 5.53
with the NICA model. However, the results with the LF model were obtained by introducing only one metal ionspecific parameter, in addition to parameters that are required for the description of the proton binding. If one assumes only binding to the carboxylic type groups in the NICA model, a description of similar quality is obtained as in the approach of Milne et al. (22). The difference between the two approaches is less than it seems. The non-ideality was accounted for by the use of the cylindrical doublelayer model, leading also to an electrostatic correction that is essentiallythe same for Cd and Ca since both are bivalent ions. Also in the NICA model, the non-ideality term for Cd and Ca are quite similar (nCd = 0.78, nca= 0.79). The value of the heterogeneity parameter p in the NICA approach is comparable to the value of the heterogeneity parameter in the LF approach. A n advantage of the NICA approach is that the correction for non-ideality is mathematically much simpler than the use of the cylindrical (or spherical) doublelayer model. The NICAmodel shows its particular strength mainly in the description of the copper binding data. These data could not be described satisfactorily with the competitive LF model. The NICA approach shows that the nonideality parameter ni for copper differs significantly from the same parameters for cadmium and calcium. The electrostatic correction that was applied by Milne et al. (22) cannot account for a difference in non-ideality for different bivalent ions. The reason for the difference in the nonideality parameter may be that the affinity distribution as used for protons does not fully correspond with the affinity distribution for the copper binding sites. The NICA model can account for such a difference. Comparison of the median affinity constants derived from our model with values achieved by other workers is encouraging. Tipping and Hurley (15) calculated constants for the equilibrium expression: RIH Mz+ f H+. When our data is expressed in the same way (Table 41,the results indicate that the constants are in the same range as those of the Tipping and Hurley (15) study. It should be remembered, however, that the electrostatic interactions are accounted for differentlyin the two models. Tipping and Hurley (15) correct explicitly for the electrostatics, while in our model the electrostatic interactions affect both niand K . Ifwe were to apply a correction factor, the constants would have smaller values and should result in a better agreement between the two studies for both the first and second peaks. Predictive Capability of the Model. The NICA model has demonstrated that it can successfully describe experimental metal binding data at different pH values and for a wide range of free metal concentrations. It is of interest to know whether it is possible to accurately predict an unknown adsorption experiment at a different pH. Such a predictive ability would be of great help for future
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experimental work or for sound risk assessment in the natural environment. To test the predictive ability, two different approaches were applied: interpolation and extrapolation. In order to test the ability of the NICA model to interpolate values, two extreme pH experiments were used in order to derive a new set of parameters for the prediction. The parameter values derived for Cu, Cd, and Ca (not shown) were similar those given in Table 3, Section A and accordinglythe interpolated results are in good agreement with experimental data. Next , the ability of the NICA model to extrapolate is tested by using the two lowest pH experiments (for example: 4 and 6 for Cu and Cd) or the two highest pH experiments to derive new parameters values. Some discrepancy is observed between the presently derived parameters and those listed in Table 3, Section A. For example, Cd parameters for the phenolic type of site are always smaller (nCd,2 = 0.23) and the errors associated with the parameters are also much higher (50.1-0.2). Consequently,the agreement between the extrapolatedsimulation and the experimental data was not as good as was achieved using interpolation. For example, the Cu binding is overestimated by a factor of 1.7. Thus, if an order of magnitude estimate of the binding is needed, then either extrapolation or interpolation using the NICA model will give reasonable results. Using data from only two experiments, one at low pH and one at high pH (in order to take into account the binding due to both classes of sites (carboxylicand phenolic)), the NICA model is able to make useful predictions of the binding under a wide range of intermediate conditions. Xue and Sigg (46) have suggested that the very low concentration of free Cu2+ions observed in Lake Greiffen is due to the high concentration of strong organic ligands. However, the measured copper speciation in Lake Greiffen is in accord with the copper binding to PPHA. Assuming that the DOC in Lake Greiffen would exhibit a copper binding behavior that is similar to the behavior of PPHA, the free copper ion concentration that would be expected can be estimated from our data. Assuming that practically all the copper in the lake water is bound to DOC, knowing that the pH is around 8, DOC is 3.5 mg L-l, and total dissolved copper is 10 nmol L-’ (461, a free copper concentration can be derived from Figure 5 of around 10-l5 mol L-l. This estimation is in excellent agreement with the value found experimentally by Xue and Sigg (46).The chemical composition of Lake Greiffen is quite different from the conditions for which the data of Figure 6 have been obtained. Notably, the salt level in the lake is much lower, and calcium ions are present. The lower salt level would promote copper binding, whereas the presence of calcium would decrease the copper binding. Although our estimate ofthe speciation of Lake GreBen can be considered a rather rough first-order approach, its result is still quite encouraging. The results suggest that humic and or fulvic acids in lake waters are very important in determining the bioavailability of ions like copper in these systems. With the parameter values obtained in this study, the competition between more than one divalent cation for binding to PPHA can be predicted with the NICA model. A start has been made to collect experimental results for such systems. Initial experimental results are in reasonable agreement with model predictions. 466
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Conclusion The non-ideal competitive adsorption (NICA) model presented here is able to describe the binding of a variety of ions (H, Ca, Cu, Cd) on a purified peat humic acid. The models fits the data reasonably well over a wide range of free metal ion concentrations ranging from pMe2+= 14 up to pMe2+= 2. This is achieved over a wide pH range (4 pH 5 101, which covers the range found in most natural environments. The results indicate that the binding of the metals to humic acid is strongly influenced by both the chemical heterogeneity of the humic material and ionspecific non-ideality effects. For monocomponent adsorption, this implies that the apparent heterogeneityis different for each metal. The model best describes the binding by assuming the presence of two major classes of metal complexing sites, which are assumed to correspond with carboxylicand phenolic type surface groups. The bimodal NICA model can be simplified to a monomodal model if one is interested in the modeling of pH-dependent metal ion binding over a narrow range of conditions. For conditions of constant pH and low metal ion concentration, the NICA model can be simplified to the classical twoparameter Freundlich isotherm. It is therefore in accord with an extensive literature for trace metal sorption by soils and sediments which has frequently demonstrated the applicability of the Freundlich isotherm under these conditions. The model results indicate that the phenolic type sites contribute significantly to the binding behavior at very low concentrations of free metal ions even at relatively low pH. The results obtained for copper binding can explain why the free copper concentration in surface waters is 7 orders of magnitude lower than the total dissolved copper concentration.
Acknowledgments This work was partly funded by the European Union STEP(390-0031. C.J.M. andD.G.K. contributewith the approval of the Director of the British Geological Survey (NERC).
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Received for review May 12, 1994. Revised manuscript received October 20, 1994. Accepted October 25, 1994.@
ES940290H @
Abstract published in AdvanceACSAbstrmts, December 1,1994.
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