Environ. Sci. Technol. 2009, 43, 7184–7191
Effective Affinity Distribution for the Binding of Metal Ions to a Generic Fulvic Acid in Natural Waters CARLOS REY-CASTRO,† SANDRINE MONGIN,† ´ SAR HUIDOBRO,† CALIN DAVID,† CE ´ S A L V A D O R , † J O S E P L L U ´I S G A R C E ´ S,† JOSE † ‡ JOSEP GALCERAN, FRANCESC MAS, A N D J A U M E P U Y * ,† Departament de Química. Universitat de Lleida, Rovira Roure 191, 25198 Lleida, Spain, and Physical Chemistry Department and Research Institute of Theoretical and Computational Chemistry (IQTCUB) of Barcelona University. C/ Martí i Franque´s 1, 08028 Barcelona, Spain
Received October 24, 2008. Revised manuscript received January 9, 2009. Accepted January 13, 2009.
The effective distribution of affinities (Conditional Affinity Spectrum, CAS) seen by a metal ion binding to a humic substance under natural water conditions is derived and discussed within the NICA-Donnan model. Analytical expressions for the average affinity of these distributions in general multi-ion mixtures are reported here for the first time. These expressions enable a simple evaluation of the effect of all interfering cations on the affinity distribution of a given one. We illustrate this methodology by plotting the affinity spectra of a generic fulvic acid for 14 different cations in the presence of major inorganic ions and trace metals at pH and concentration values representative of a river water. The distribution of occupied sites and their average affinity at the typical freshwater conditions are also reported for each ion. The CAS allows us to distinguish three groups of cations: (a) Al, H, Pb, Hg, and Cr, which are preferentially bound to the phenolic sites of the fulvic ligand; (b) Ca, Mg, Cd, Fe(II), and Mn, which display a greater effective affinity for carboxylic sites, in contrast to what would be expected from their individual complexation parameters; and (c) Fe(III), Cu, Zn, and Ni, for which phenolic and carboxylic distributions are overlapped.
Introduction The binding of cations to natural ligands plays a key role in the circulation of metals in natural systems (1). Multicomponent isotherms are widely used to describe this binding since they provide analytical expressions of the coverage of each component in terms of the concentration of all the components present in the system. The most popular models in the context of metal binding in environmental systems are models V/VI (2), which use a discrete distribution of affinities, and the Non-Ideal Competitive Adsorption Isotherm (NICA) (3-6), which uses a continuous distribution of affinities. The NICA-Donnan model is a combination of the NICA isotherm for the description of the chemical binding * Corresponding author phone: 34-973-702529; fax: 34-973238264; e-mail:
[email protected]. † Universitat de Lleida. ‡ Barcelona University. 7184
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to a heterogeneous ligand and the Donnan model for the description of polyelectrolytic effects. This model accurately describes the competitive behavior in synthetic solutions (7-9) and it provides reasonable predictions of in situ metal speciation measurements in freshwaters (10, 11). In the affinity spectrum approach, heterogeneity is described by modeling the ligand as a set of independent sites, each of which obeys the Langmuir isotherm with a given affinity. In competitive systems, this distribution is known as the multidimensional affinity spectrum, p(logk1, logk2, etc. ), which indicates the relative abundance of sites with logk1 affinity for component 1, logk2 affinity for component 2, and so on (12, 13). Complementary, the Conditional Affinity Spectrum (CAS) has been introduced (14) as a way of assessing the effective distribution of affinities seen by a metal under the restriction of fixed proton concentration. One advantage is that CAS can be defined also in some cases where there is no multidimensional affinity spectrum. In particular, NICA isotherm has a CAS for any set of binding parameters (15, 16), whereas the existence of multidimensional spectrum is limited to some combination of these parameters (12). CAS provides very useful information, since changes in the spectra allow the assessment of the effective binding strength and heterogeneity seen by the probed ion as a function of the concentration of competing species (e.g, H+). A recent application of this formalism to Pb binding by humic acid (15) interpreted the variation of the average and variance of the CAS with pH in terms of the exchange binding energy and degree of correlation between the binding energies of Pb2+ and proton ions to the humic sites. The correspondence between tabulated NICA binding parameters for a given ion and the average ligand affinity displayed for this ion in a multicomponent system is not straightforward. In absence of competing cations, NICA isotherm leads to a Sips distribution of affinities. However, the average and variance of this distribution differ from the affinity average and variance experienced by the same cation in a competing mixture. Moreover, the detailed prediction of the ion binding behavior in the mixture requires the knowledge of the whole spectrum (not only its average and variance), and its dependency with the medium composition. This would allow calculations such as fraction of metal bound at trace level concentrations, distribution of occupied sites, prediction of the effect of sudden changes in composition like those resulting from a pulse of contaminant due to waste spills, etc. The aim of the present work is to provide analytical expressions for the CAS underlying NICA isotherm for humic matter in the presence of a general mixture of competing cations. Analytical expressions for the average affinity will also be reported. This general formalism can be useful to assess the binding characteristics of humic matter in a system close to natural conditions and to discuss the relative effect of major and minor cations. To exemplify this, we report and discuss the CAS of 14 major and minor cations calculated for a generic description of fulvic acid in conditions representative of a typical natural freshwater.
Theoretical Background CAS Underlying NICA Isotherm in a Mixture of Competing Ions. Since proton titration curves of humic matter (fulvic or humic acid) often show a double wave shape, NICA isotherm is usually written as a bimodal distribution when applied to these kind of complex ligands (5-7, 17-22). The first wave is associated to “carboxylic” sites, whereas the 10.1021/es803006p CCC: $40.75
2009 American Chemical Society
Published on Web 03/05/2009
second one is related to “phenolic” sites, although the chemical description of the functional groups involved in each distribution is much more complex. For each of these distributions, the fraction of sites occupied by species i is given by NICA isotherm as (kj i,jci)ni,j
θi,j(cH, c1, c2, ..., cn) )
×
n
(kj H,jcH)nH,j +
∑
(kj m,jcm)nm,j
m)1 n
((kj H,jcH)nH,j +
∑ (kj
m,jcm)
nm,j pj
)
m)1
(1)
n
1 + ((kj H,jcH)
nH,j
+
∑ (kj
m,jcm)
nm,j pj
)
This means that the conditional affinity of a site for ion i is just its affinity in absence of interfering ions minus a term that accounts for the energy involved in the removal of all the competing cations from this site. The advantage of the restriction cm ) cnt ∀m * i is that it allows us to obtain the CAS by applying inversion formulas for monocomponent isotherms (24, 25). This procedure was used in a previous work (15) to obtain an analytical expression for the CAS underlying the NICA isotherm in mixtures of two competing species (H+ and a metal ion). The same procedure is generalized in the present work to multicomponent systems (mixtures of n ions), leading to an analytical expression for the corresponding CAS. The derivation of this expression is detailed in Appendix 1 in the Supporting Information (SI). The final formula reads
m)1
where subscript j refers to the modal distribution (1: carboxylic and 2: phenolic). In this way, the total amount of species i bound to the humic ligand, Qi, is Qi ) Qmax i,1θi,1 + Qmax i,2θi,2
(2)
Equation 1 is valid for a generic mixture of competing species composed of protons (H) and n metal cations. Parameters ni,j (0 < ni,j e1) are related to binding nonideality of ion i and modal distribution j, whereas pj (0 < pj e1) accounts for the intrinsic heterogeneity of the modal distribution j and it has a common value for all the cations (5, 6, 21, 23). Finally, kjI,j are adsorption parameters, and ci represent the concentrations. Notice that NICA isotherm is usually combined with the Donnan electrostatic model. In that case the isotherm accounts for the intrinsic (chemical) binding only, i.e., the binding energies free of electrostatic contribution, and therefore, the concentrations ci in eq 1 are the values in the Donnan phase. Notice also that the coverages θi,j, as given in eq 1, are normalized to 1, whereas the maximum amounts of metal and proton bound are related by Qmax H,j nH,j ) ;i ) 1, 2, ..., n Qmax i,j ni,j
ln(10) π 1 × ni,2 ni,1 Q + Q nH,1 max H,1 nH,2 max H,2 n p ni,j (kj i,j /k i) i,jMi,jj-1 Qmax H,j [sin(πni,j - (1 2pj pj nH,j 1 + Mi,j + 2Mi,j cos(pjφi,j)
p(log ki ;cH, cm*i)cnt) )
2
∑ j)1
(
(
)
)
pj pj)φi,j) + Mi,j sin(πni,j - φi,j)] (6)
where Mi,j(ki ;cH, cm*i) )
[
{(kj H,jcH)nH,j +
∑ (kj
m,jcm)
nm,j
+ (kj i,j /ki)ni,jcos(πni,j)}2
m*i
+{(kj i,j /ki)ni,jsin πni,j}2
]
1/2
(7)
and (kj H,jcH)nH,j +
∑ (kj
nm,j
m,jcm)
+ (kj i,j /ki)ni,jcos(πni,j)
m*i
cos(φi,j) )
Mi,j
(3)
(8)
in order to ensure thermodynamic consistency of the NICA isotherm (5). Therefore, ni,j can also be interpreted as stoichoimetry-related parameters, since they determine the maximum ratio of bound metal vs. proton ions. If we restrict to a fixed concentration of all competing cations except one, e.g., ion i, then the competitive isotherm becomes monocomponent and the corresponding affinity spectrum, p(logki’; cH,cm * i ) cnt), is defined from
Equation 6 constitutes a general explicit expression for the CAS underlying NICA isotherm in a complex mixture of cations. This formula can be easily implemented in a standard spreadsheet. Average of the CAS. Although the knowledge of the whole CAS is required for a full description of the binding behavior, important information is conveyed by the first moment of the distribution. This can be evaluated numerically once the spectra are known, but an explicit analytical expression for the calculation of the CAS average is provided below:
θi )
∫
∞
-∞
p(log k′i ;cH, cm*i ) cnt)
kici 1 + kici
dlog k′i ;
2
m ) 1, 2..., n (4)
〈log k′i〉cH,cm*i)cnt )
∑ j)1
where k′i labels the effective or conditional affinity seen by ion i, and p(logki’; cH,cm * i ) cnt) indicates the relative abundance of available sites having this affinity. From now on, p(logki’;cH,cm * j ) cnt) will be denoted as the Conditional Affinity Spectrum (CAS). In those cases where the multidimensional affinity spectrum applies, a specific affinity for every ion can be assigned to each site and k′i can be defined as (14)
(
log k′i ) log ki - log 1 + kHcH +
∑k
)
mcm
m*i
where the k are site-specific binding constants.
(5)
(
log kj i,j -
(
))
ni,j Q nH,j max H,j × ni,2 ni,1 Q + Q nH,1 max H,1 nH,2 max H,2
1 log[1 + ((kj H,jcH)nH,j + ni,jpj
∑ (kj
m,jcm)
m*i
nm,j pj
) ] (9)
The derivation of this expression can be found in Appendix 2 of the SI as a generalization of the procedure described in a previous work (16) for two-component systems. This expression indicates that the average effective affinity for ion i is just the average affinity of the ligand in absence of competing ions (represented by the NICA binding parameter logki,j) minus one term that reflects the ion exchange work, i.e., the work needed to extract successively the other competing cations (i.e., ions m * i) from the site. VOL. 43, NO. 19, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Composition of the River Water Sample and Speciation Results Obtained with Visual MINTEQa
Ca2+ (CO3)T (SO4)T Mg2+ Na+ ClNO3K+ Fe3+ Al3+ Cu2+ Zn2+ Ni2+ Pb2+ Cd2+ pH I Fulvic acid
total concentrationb (mol/L)
ci, free ion concentration (bulk)d(mol/L)
1.56 × 10-3 1.20 × 10-3 6.23 × 10-4 3.00 × 10-4 2.60 × 10-4 2.14 × 10-4 6.60 × 10-5 3.90 × 10-5 1.10 × 10-6 5.20 × 10-7 5.00 × 10-8 5.00 × 10-8 1.00 × 10-8 5.00 × 10-9 5.00 × 10-9 7.00 6.4 × 10-3 mol/Lc 0.5 mg/L
1.46 × 10-3 9.82 × 10-4 5.21 × 10-4 2.84 × 10-4 2.59 × 10-4 2.13 × 10-4 6.58 × 10-5 3.89 × 10-5 1.20 × 10-14 7.39 × 10-12 6.19 × 10-9 4.51 × 10-8 8.54 × 10-9 3.82 × 10-10 4.28 × 10-9
cD,i, free ion concentration in Donnan phased(mol/L) 3.12 × 10-1 6.08 × 10-2 3.80 × 10-3 1.46 × 10-5 4.49 × 10-6 5.69 × 10-4 3.75 × 10-11 2.32 × 10-8 1.33 × 10-6 9.67 × 10-6 1.83 × 10-6 8.18 × 10-8 9.17 × 10-7 -log cD,H ) 5.80
a The ionic species are listed in order of total concentration. b The composition of major ions is taken from analysis of filtered (0.2 µm) water from Arve River (27), whereas Cu, Zn, Ni, Pb, and Cd trace metals were included at representative concentrations; c Ionic strength calculated from conductivity as I ) 1.6 × 10-5 × (κ/mScm-1) following ref 34. d Calculated using the standard database of VMinteq with the recent Fe(III) binding parameters derived by Hiemstra and Van Riemsdijk (26) and the NICA-Donnan generic parameters of Milne et al. (22) for the rest of ions. The electrostatic accumulation factor in these conditions is log(cD,i/ci)zi ) 1.17 × zi, with zi the charge of ion i. Formation of solid Fe/Al hydroxydes is not considered.
Obviously, the order by which the cations are considered is not relevant. Equation 9 shows that the effect of a competing cation m on the average affinity for ion i mainly depends on three factors: the product kjm,j cm, the values of nm,j and ni,j, and pj. Indeed, the average affinity for i is obviously weakened by an increasing concentration of interfering ions in the medium. A similar effect follows an increase of logkjm,j since it represents the mean energy to be expended by ion i in removing ion m. Likewise, an increase in the ratio nm,j over ni,j (which is associated to the relative number of functional groups involved in the binding of ions m and i, see eq 3) leads to a faster decrease in the CAS average of ion i. Also the shape of the CAS is influenced by the concentration of the competing cations. Restricting ourselves to the case where the multidimensional affinity spectrum applies, eq 5 can be helpful in recalling that not all the sites with affinity ki for ion i experience the same decrease in the metal affinity due to the presence of another cation m. Rather, sites with the same absolute affinity ki for ion i may display different affinities km for the competing ions, within a range that can be narrow or wide depending on the high or low correlation of the binding energies, respectively. Therefore, a change in the shape of the CAS distribution takes place as the concentration of interfering ions increase since each particular kind of sites is “scattered” in a range of affinities due to the different extent of the competition effect for that site. However, even if the system exhibits full correlation of binding energies among the sites, there is still a change in the shape of the CAS of ion i as the concentration of ion m changes. Indeed, if ki ∝ km then eq 5 implies that sites with high affinity will display a larger shift than sites with low affinity and, consequently, the peak of the CAS for ion i will become narrower and taller as the concentration of m increases.
Results and Discussion CAS of a Generic Fulvic Acid in a Representative Sample of Natural Water. In order to describe the competitive ion binding to a model fulvic acid dissolved in a multicomponent mixture with a composition resembling a typical natural 7186
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freshwater, we adopt the set of generic NICA-Donnan parameters reported by Milne et al. (22). An exception is made for the binding of Fe(III), for which we use the more recent NICA parameters proposed by Hiemstra and Van Riemsdijk (26). The evaluation of the CAS requires the previous calculation of the local concentrations of all ions in the Donnan phase. In order to estimate these concentrations, we consider an aqueous system with the composition listed in Table 1 at pH 7. The concentrations of major ions correspond to a filtered water sample from Arve River (Switzerland) (27, 28). Concentrations below 1 µmol/L of several trace metals (Cu, Zn, Ni, Pb, and Cd) were added to simulate a low level of contamination. Dissolved organic matter, consisting exclusively of fulvic acid, was considered at a concentration of 0.5 mg/L. For simplicity, no humic acid was considered. This concentration lies below the values of total organic carbon reported for Arve River samples. Speciation calculations at 298 K were carried out at fixed pH and ionic strength, using Visual MINTEQ (29) with the standard thermodynamic database for the inorganic species. The Specific Ion Interaction theory was considered for the calculation of the activity coefficients (30). The ionic strength value was estimated from the reported experimental conductivity of 400 µS/cm (28). Given the relatively high total Fe(III) and Al concentrations, the speciation calculations suggest supersaturation of iron or aluminum hydroxides. For simplicity reasons, the solubility equilibria of these solid phases were not accounted for in the CAS shown in the present work. The solubility equilibrium with atmospheric CO2 was not considered in the calculations. The resulting local concentrations in the Donnan phase are listed in the last column of Table 1. Notice that, due to the relatively high electrostatic charge of the fulvic molecule, the cation concentrations are significantly higher in the Donnan phase than in bulk solution. For instance, the local pH turns out to be -logcD,H ) 5.80, whereas the bulk value is pH 7. Finally, the estimated Donnan concentrations cD,i together with the chosen intrinsic NICA parameters (22, 26) were used to calculate the CAS of each ion of interest using eq 6. Some
FIGURE 1. Effect of the competitive medium on the effective Pb binding affinity of a generic fulvic acid. Dashed line: affinity spectrum in absence of competing ions; solid line: CAS in natural water calculated using eq 6 with generic NICA-Donnan parameters (22) except for Fe(III) (26) and speciation results listed in Table 1. In this case, Pb binding takes place preferentially on phenolic sites. The contour of the shaded area in the inset shows the density of fulvic sites occupied by Pb2+ at cD,Pb ) 8.18 × 10-8 mol/L, as given by eq 11. Note the enlargement of vertical axis, according to the low degree of Pb-fulvic complexation.
FIGURE 2. Effect of the competitive medium on the effective Ca binding affinity spectra of a generic fulvic acid. The phenolic distribution of the CAS (left peak in solid line) shows much lower affinity than the carboxylic one, in contrast with the spectrum in absence of competing ions (dashed line). Consequently, metal binding will preferentially take place at carboxylic sites. The shaded area in the inset shows the density of fulvic sites occupied by Ca2+ at cD,Ca ) 3.12 × 10-1 mol/L. selected results are shown in Figures 1-3, and the complete set of plots can be found in Appendix 3 of the SI. These affinity spectra depict only the distribution of chemical energies involved in the cation binding to the fulvic ligand. The distribution of total binding energy experienced by the ion in the test natural water can be assessed by adding the corresponding electrostatic contribution (i.e., by shifting the CAS toward higher affinities). At the actual conditions of the test natural water, the electrostatic Boltzmann factor has a value of log(cD,i/ci)zi ) 1.17 × zi (seeTable 1), where zi is the charge of ion i. For the typical composition of unpolluted
natural waters, this factor is almost independent of the concentration of the probed ion. Figure 1 shows the application of the CAS methodology to the case of Pb binding by a generic fulvic acid in a freshwater sample. Notice the evolution of the spectra from the monocomponent system to the multicomponent mixture. In absence of competing ions, the Pb affinity spectrum corresponds to two Sips distributions centered at logkPb,1 and logkPb,2 (dashed line). This information does not provide a straightforward perception of how the Pb-fulvic binding behavior will be in the multicomponent system. On the other VOL. 43, NO. 19, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. Effect of the competitive medium on the effective Zn binding affinity spectra of a generic fulvic acid. Dashed line: spectrum in absence of competing ions; solid line: CAS in the freshwater showing overlapped phenolic and carboxylic distributions. The shaded area in the inset shows the density of fulvic sites occupied by Zn2+ at cD,Zn ) 9.67 × 10-6 mol/L.
TABLE 2. Average Affinity Values of the Generic Fulvic Acid for the Different Cations carboxylic sites log Ca2+ Mg2+ Fe3+ Al3+ H+ Cu2+ Zn2+ Ni2+ Pb2+ Cd2+ Cr3+ Fe2+ Hg2+ Mn2+
a
ki,1
-2.13 -2.1 2.7b -4.11 2.34 0.26 -3.84 -2.07 -1.16 -0.97 2.8 -1.02 3.8 -1.55
phenolic sites
〈logk′i,1〉c
〈logk′i,1〉occd
-2.2 -2.2 2.5 -4.2 2.3 0.1 -3.9 -2.2 -1.3 -1.1 2.6 -1.2 3.6 -1.6
-0.1 0.6 11.1 8.0 5.6 5.9 4.2 5.1 6.6 5.2
log
a
ki,2
-3.0 -2.4 8.3b 12.16 8.60 8.26 -0.73 2.03 6.92 0.50 20 -1.1 24 -1.1
global
〈logk′i,2〉c
〈logk′i,2〉occd
〈logk′i〉c
〈logk′i〉occd
-5.8 -6.2 -1.5 5.1 6.5 2.1 -4.4 -2.2 3.7 -4.0 11.7 -5.5 15 -5.1
-1.2 0.8 12.0 8.8 6.7 6.6 4.5 5.6 6.3 6.0
-2.9 -2.9 1.9 -2.6 3.3 0.5 -4.0 -2.2 -0.1 -1.6 4.2 -2.6 5.6 -2.2
-0.1 0.6 11.2 8.8 6.6 6.3 4.2 5.2 6.3 5.2
a Average of the intrinsic spectrum (data from Milne et al. (22) except for that described in footnote b. b Fe binding parameters taken from Hiemstra and Van Riemsdijk (26)). c Average of the CAS at conditions listed in Table 1, calculated using eq 9. d Average of the effective distribution of occupied sites calculated using eq 12 for the conditions listed in Table 1. The total concentration of the four last ions (and hence their complexation by fulvic acid) is considered negligible in the natural water.
hand, the CAS (solid line) shows in a direct way the joint influence of the background ions on the effective binding affinities of the ligand for Pb. The shift of the CAS toward lower affinities reflects a significant competition effect. However, only the phenolic distribution narrowed and shifted noticeably indicating that (i) only these sites are occupied by the competing ions at the tested conditions; and (ii) the sites with high affinity for the competing ions also display a high affinity for Pb, which is a consequence of the large correlation between the binding energies of the sites among different ions that results from the NICA description of the experimental data. At the studied pH, the most important influence from the medium cations on the overall Pb CAS is due to proton ions and, to a lesser extent, Al. The large value of the adsorption parameters (logkjH,2 ) 8.60 and logkjAl,2 ) 12.16, respectively), along with the relatively high Donnan phase concentration of these ions, lead to a significant coverage of phenolic sites and a large ion exchange energy required to remove the competing species, which 7188
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justifies the remarkable shift of the Pb CAS toward lower affinities. Nevertheless, the shift in the phenolic peak is not enough to reverse the order of the affinities of both distributions and the binding of Pb ions is expected to take place preferentially on the phenolic sites. Patterns similar to Pb, i.e., a double peak shape (with phenolic sites displaying a remarkably larger affinity than the carboxylic ones), are also observed in the CAS of Al, Cr, H, and Hg (see Appendix 3 in the SI). However, other cations exhibit, in freshwater conditions, a CAS with a double peak shape where the order of affinities is the opposite to what is expected from their intrinsic binding parameters. This is the case of Ca (Figure 2), Cd, Fe(II), Mn, and Mg (see Appendix 3 in the SI). Notice that in these CAS the carboxylic distribution remains almost unaltered by the presence of competing cations, whereas the shift of the phenolic distribution is so considerable that it becomes much weaker than the carboxylic one (15). Hence, the binding will take place preferably on the carboxylic sites, and only at very large concentrations
FIGURE 4. Values of (k¯m,jcm)nm,j, i.e., the contribution term to the CAS average in eq 9, corresponding to each competing ion at its actual concentration in the test natural water (Table 1). The higher the value of this term, the higher the competitive effect due to this ion.
FIGURE 5. Fractional occupation of the carboxylic and phenolic site distributions of the generic fulvic acid in the test water system described in Table 1. (probably unrealistic) can the phenolic sites be involved in metal binding. Consequently, the specific parameters that characterize the phenolic distribution have little relevance for the study of complexation of these ions by fulvic acids in natural conditions. These results agree, e.g., with the assumption of Pinheiro et al. (8) about the Ca binding to fulvic acid taking place mainly on the carboxylic sites. The third kind of spectra corresponds to Zn (Figure 3), Cu, Fe(III), and Ni (see the SI), which consist of a single peak. In these cases, the effective affinity distribution is monomodal and, therefore, the binding of metal ions is shared more or less equally between both kinds of sites. The average values of the affinity spectra are listed in Table 2 for all the ions considered in this study. Notice that for both distributions the CAS average (which depends on the system composition) is lower than the corresponding NICA parameter logki,j associated to the average affinity in absence of competing ions. Quantitatively, this effect is described by eq 9. In this expression, the specific contribution of each interfering species is given by (km,jcm)nm,j. The values of this term for every ion are displayed in Figure 4. Except for Mg and Ca, the competition effect is several orders of magnitude more intense on the phenolic sites than on the carboxylic ones. This leads to the reversal in the affinity order of both distributions that was described above for some cations. The influence of proton ions is, at this pH, the most
important contribution (particularly in the phenolic sites), followed by Al and Cu, whereas the effect of major cations such as Mg2+ or Ca2+ is relatively small despite their high concentration. Notice that, at these conditions, the effect of Fe3+ ions is several orders of magnitude lower than other medium ions. Consequently, the inclusion of the precipitation equilibrium of ferrihydrite does not exert a noticeable influence over the CAS of other ions at this pH. On the other side, the consideration of aluminum hydroxide solubility equilibria may lead to somewhat different results, particularly for the H+ CAS. Taking into account Figure 4, the contribution of the rest of competing cations other than H and Al can be neglected in eq 9, leading to this approximate expression for the average affinity of the phenolic distribution 〈log k′i,2〉cH,cm*i)cnt ≈ log kj i,2 -
1 log[(kj H,2cH)nH,2 + ni,2 (kj Al,2cAl)nAl,2] (10)
Note that cations with a lower value of ni,2 (generally, ions with larger charge) will experience a larger influence of the competitive environment. Let us compare, for instance, the binding of Fe3+ (nFe(III),2 ) 0.23) and Pb2+ (nPb,2 ) 0.69) to the phenolic distribution. From Table 2 we see that the shift from log kji,2 to 〈logk′i,2〉 is -9.8 and -3.2 log units, VOL. 43, NO. 19, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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respectively, which results in a reversal of the affinity order between both metals. Since the most important influences of the environment in both cases are due to H and Al, the observed difference comes from the respective values of ni,2, which is a parameter presumably related with stoichiometry. Hence, this result agrees with the expected trend of an increasing competitive effect in those cases with larger ion exchange ratios. Despite their usefulness, the average values of the CAS are only rough estimates of the binding strength of the cation of interest since they do not necessarily reflect the energy exchanged in the sites that are actually involved in the binding. Indeed, the CAS provides the relative amount of binding sites of each affinity that are available for a given ion irrespective of its concentration. The distribution of occupied sites at the actual concentration of ion i, can be easily calculated from the CAS as follows: pocc(log ki, ci) ) p(log ki ; cH, cm*i ) cnt)
kici 1 + kici
(11)
∫
∞
-∞
log kipocc(log ki, ci)dlog ki
(12)
Table 2 lists the values of 〈logk′i〉occ for every ion i at its concentration in the freshwater. Compare, for instance, the average value of the phenolic CAS of Pb (3.7 in log units) with the 〈logk′Pb,2〉occ value of 6.3. Note that the values of 〈logk′i,j〉occ are higher than the CAS averages for all the cations considered. Figure 5 shows the overall occupation of carboxylic and phenolic sites under natural water conditions. Notice that the phenolic sites are almost completely occupied, whereas most of the carboxylic sites are free (ionized). The binding of protons represents the main fraction in the phenolic distribution, followed by Al. The inclusion of an equilibrium control for free Al3+ in solution by colloidal forms of aluminum hydroxide at pH 7, may have a significant effect over the fractional occupation of this ion. The reliability of the conclusions and observed trends reported here depends on the accuracy of the NICA-Donnan parameters adopted. In particular, the speciation results concerning Fe(III) must be considered with caution due to the relatively large uncertainty of its binding parameters, resulting from the extremely limited amount of reliable experimental data available. In fact, the recently reported parameters of Hiemstra and Van Riemsdijk (26) for Fe-fulvate complexes contrast strikingly with the values previously estimated by Milne et al. from empirical correlations (22). Both sets of data lead to remarkably different descriptions of the competition effects in the freshwater (see the SI for a comparison). Hence, the need for more accurate experi7190
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Acknowledgments We gratefully acknowledge support of this research by the Spanish Ministry of Education and Science (Projects CTQ2006-14385 and CTM2006-13583) and from the “Comissionat d’Universitats i Recerca de la Generalitat de Catalunya”. S. Mongin was supported by an FPI-MEC grant from the Spanish Government.
Supporting Information Available
These distributions are compared with the CAS of each ion in Figures 1-3. From this equation it is clear that, when the probed ion is at a concentration of ci ) 1/k′i, the sites with an affinity of logk′i are half-occupied. By definition, the integral of pocc(logki’,cPb)over the whole domain of the CAS gives the metal coverage, θi, at concentration ci (compare eqs 4 and 11). Let us consider, for instance, the distribution of sites occupied by Pb in natural water conditions (see inset of Figure 1). It can be observed that the fraction of fulvic sites complexed by Pb is very small (θPb ) 1 × 10-3), consistently with the negligible value of the CAS function at logk′Pb ) -log cD,Pb ) 7.1 (local Pb2+ concentration in Donnan phase, see Table 1). Due to its very low coverage, the affinity of the sites actually involved in Pb binding is much higher than the average value of the Pb CAS. To quantify the average affinity of occupied sites, we define 〈log ki′ 〉occ )
mental results about the characterization of the humic matter-Fe(III) complexation is largely justified, as supported by a number of papers published recently (31-33). Also the influence of not very well characterized amorphous iron/ aluminum hydroxides may be certainly significant and requires further study. Beyond the inherent interest of these results for model freshwater systems, we highlight the applicability of the CAS methodology to the description and understanding of metal-humic matter interaction in multimetal environments such as natural waters.
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Appendices containing the detailed derivation of the analytical equation of the CAS underlying the bimodal NICA isotherm, eq 6, the calculation of the CAS average, eq 9, the additional plots of the CAS for the different ions in the test natural water at pH 7 and a spreadsheet implementation of the CAS calculation. This material is available free of charge via the Internet at http://pubs.acs.org.
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