Voltammetric Analysis of Heterogeneity in Metal Ion Binding by

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Environ. Sci. Technol. 2001, 35, 1097-1102

Voltammetric Analysis of Heterogeneity in Metal Ion Binding by Humics F R A N C I S C O B E R B E L , * ,† J O S EÄ M A N U E L D IÄ A Z - C R U Z , † CRISTINA ARIN ˜ O,† MIQUEL ESTEBAN,† FRANCESC MAS,‡ J O S E P L L U IÄ S G A R C EÄ S , ‡ A N D J A U M E P U Y § Departament de Quı´mica Analı´tica and Departament de Quı´mica Fı´sica, Universitat de Barcelona, Martı´ i Franque`s 1, E-08028 Barcelona, Spain, and Departament de Quı´mica (ETSEA), Universitat de Lleida, Av. Rovira Roure 177, E-25198 Lleida, Spain

The complexation of Cd, Pb, and Cu by fulvic acids at a fixed pH and ionic strength is studied by means of different voltammetric techniques at any metal-to-ligand ratio. When using Reverse Pulse Polarography (RPP) the complex species are electrochemically labile and not subject to significant electrodic adsorption. RPP titrations of fulvic acid with metal ions are interpreted on the basis of a recently proposed analytical expression for limiting currents valid for fully labile heterogeneous complexation. The voltammetric data are transformed into the corresponding binding curve, i.e., the fraction of occupied sites vs free metal concentration. Finally, the competition between metal ions and protons in their interaction with the fulvic binding sites as well as the concomitant polyelectrolytic effects are analyzed in terms of the NICCA-Donnan model. The results show that voltammetric techniques can be applied to the studies of heterogeneous complex systems in a broad range of metal-to-ligand ratios.

Introduction Complexation of metal ions by humic matter (HM)sincluding both humic and fulvic acidsshas become an important topic in environmental studies because its understanding is closely related to the bioavailability, toxicity, and mobility of metals in natural systems (1-3). So, it has been widely accepted that HM plays a key role in the regulation of metal ions and other pollutants in the environment (3). HM originates from complex processes in which degradation and excretion products of living organisms produce disperse mixtures of natural organic polyelectrolytes that possess a great number of different functional groups, which are responsible for their chemical heterogeneity. HM is of a polyelectrolytic nature, and its affinities for protons and metal ions strongly depend on the amount of deprotonated groups, i.e., on the effective site density. The ionic strength governs the swelling and shrinking of HM entities, thus setting the actual spatial conformation, which eventually determines relevant hydrodynamic properties such as the diffusion coefficient. * Corresponding author phone: (34) 93 402 12 86; fax: (34) 93 402 12 33; e-mail: [email protected]. † Departament de Quı ´mica Analı´tica, Universitat de Barcelona. ‡ Departament de Quı ´mica Fı´sica, Universitat de Barcelona. § Universitat de Lleida. 10.1021/es000111y CCC: $20.00 Published on Web 02/06/2001

 2001 American Chemical Society

Voltammetric techniques are outstanding in speciation studies due to (i) their high sensitivities allowing studies at natural concentration levels, (ii) the dependence of the analytical signal on the nature of the species involved, and (iii) minimum perturbation of the chemical conditions of the sample (3-5). However, interpretation of voltammetric signals obtained from natural samples is often very difficult. Up to now, most studies concerning labile speciation have been done under conditions of large excess of complexing sites over metal ions, those sites being provided by a macromolecular ligand (6-8), or with a mixture of simple ligands (9), for which homogeneous and independent complexation can be assumed. The effect of heterogeneity on the shape of the voltammetric signals for fully labile complexation was first studied by Filella et al. (10) by assuming a unimodal Freundlich isotherm. In a further study (11) this approach was applied to the characterization of Pb and Cd binding to HM. Pinheiro et al. (12, 13) used the excess-ligand expression for the limiting current to obtain the average equilibrium function, which revealed the heterogeneity of HM through its dependence on the metal concentration. However, this procedure requires a large excess of ligand, and it does not take into account the variation of the average equilibrium function along the diffusion layer. Theoretical analyses have shown that in the limit of ligand excess conditions (cM f 0) any system will eventually follow the homogeneous complexation model, for which the stability constant is independent of concentration and corresponds to the average of the intrinsic or microscopic affinities of all sites (14, 15). On the other hand, the treatment at any ligand-to-metal ratio requires the assumption of a particular model of complexation. A recently proposed methodology for the interpretation of the fully labile voltammetric measurements includes the ligand heterogeneity and provides a direct way to calculate the binding curve for labile complexes from the experimental limiting currents at different total concentrations of ligand and metal (16). Several methods are available for the analysis of binding curve data for heterogeneous ligands (5). The thermodynamical approach of the NICCA-Donnan model (13, 17-19) has been extensively applied to heterogeneous complexation, thus yielding satisfactory results in the modeling of the binding and in predicting the effects of ionic strength and competition between the several ions present in the medium by potentiometric techniques. The aim of this work is to develop and test an experimental approach, based on previous theoretical studies (16), to compute metal binding curves from voltammetric data. The approach is applied to the study of the complexation of Cd, Pb, and Cu by a commercial fulvic acid. Proton and metal ion binding information are obtained from acid-base potentiometric and metal voltammetric titrations, at given values of ionic strength, respectively.

Theoretical Formulation Computation of Binding Curves from Voltammetric Data. When heterogeneous complexation of a metal ion M to a complex ML takes place, the average equilibrium function, h (3, 10, 11)) is defined by Kc (also often denoted as K

Kc )

cML cLcM

(1)

where cML is the sum of all complexed species and cL is the VOL. 35, NO. 6, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Schematic representation of the proposed procedure for labile heterogeneous complexation data analysis. The subindex l stands for the considered site, i.e., 1 or 2 for a bimodal isotherm and i for the involved species. The difference between QmaxH and c/T,L is in the particular unit, mol kg-1 and mol L-1, respectively. sum of the concentration of the ligands. Kc increases along the diffusion layer (3, 14, 15), reaching the highest value just at the electrode surface. Under limiting diffusion conditions at the electrode surface the value of Kc coincides with the average value of all microscopic stability constants (15) cMf0

Along with Kc, the average of the diffusion coefficients of M and ML also varies along the diffusion layer due to the variation of the fraction of bound metal, which is denoted as Y ()cML/cT,M)

(

)

1 + KccL cM cML DM + DML ) DM ) cT,M cT,M 1 + KccL (1 - Y)DM + YDML (2)

where  ) DML/DM. Actually, in limiting diffusion conditions, D h varies from D h ex at the electrode surface to D h * in the bulk solution, due to the variation of the fraction of bound metal along the diffusion layer, which decreases from its value at the electrode surface (Yex ) Kc/T,L/(1+Kc/T,L)) to the one in the bulk solution (Y* ) K/c c/L/(1 + K/c c/L)). Let Ilim and I0lim label the normalized limiting current in the presence and in absence of ligand, respectively. It has been shown in ref 16 that for heterogeneous labile complexation, a good approximation for the normalized limiting current φ can be obtained for any heterogeneous complexation model in terms of a constant “effective diffusion coefficient”, D h eff, comparable to what has been deduced for excess ligand conditions (6):

φ≡

Ilim I0lim

)

( ) D h eff DM

1/2

(3)

D h eff can be developed through a polynomial expression in terms of D h ex and D h *, for which the weighting coefficients depend on the fraction of bound metal Y (16). The values of these coefficients were established by fitting of simulated data for the simplest case, i.e., the homogeneous one. For more details the reader is referred to ref 16. 1098

9

φ ) {1 - (1 - )Y*[(1 + (1 + R)Yex) (1 + R - βYex)Y* - (β - γYex)Y*2 - γY*3]}1/2 (4) where R, β, and γ were given by

K ≡ 〈k〉 ) lim Kc

D h )

The final resulting expression was

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 35, NO. 6, 2001

R(Yex) ) -0.3475 + 2.7072 exp(-2.1749Yex) + 8.7696 exp(-9.4075Yex) (5a) β(Yex) ) 3.0648 + 13.051 exp(-1.4377Yex) 163.18 exp(-11.392Yex) (5b) γ(Yex) ) -0.7045 + 53.071 exp(-5.1594Yex) + 1452.4 exp(-17.314Yex) (5c) The influence of the heterogeneous complexation model is embodied in the values of Y* and Yex obtained for certain total metal and ligand concentrations. As can be seen, eqs 4 and 5a-c give a simple polynomial expression for the limiting current in terms of , Y*, and Yex. Equation 4 can be numerically solved easily, allowing the computation of the bulk concentrations of free and bound metal at the bulk solution, from a measurement of the normalized limiting current and the knowledge of Yex and . The procedure suggested for computing the binding curve from a voltammetric titration of ligand with metal is summarized in Figure 1. It has two main steps: (i) determination of Yex from the extrapolation of the normalized current at ligand excess conditions (“voltammetry” box in Figure 1), followed by computation of R, β, and γ using eqs 5a-c [Moreover, it is necessary to estimate  value from the normalized current at very high ligand concentrations (“voltammetry” box in Figure 1).] and (ii) determination of / Y* for each set of cT,M , c/T,L values by solving eq 4, followed by computation of bound and free metal concentrations from mass balance equations (“compute Y*” box in Figure 1). NICCA-Donnan Model Outline. In the NICCA-Donnan model, the interactions between ions and humic matter are classified as specific binding (intrinsic affinity) and nonspecific binding (Coulombic interactions). The model has

been widely described in the literature (17-19), and it will not be discussed in detail here. The basic NICCA equation for the overall binding of species i in the competitive situation for a bimodal distribution (18) encompassing binding sites with a low affinity (l ) 1) or with a high affinity (l ) 2) distribution is

Qi )

∑Q

maxH,l

nH,l

l)1

∑(kh

(

(kh i,lcD,i)ni,l

ni,l

2

(

∑(kh

p,lcD,p)

np,l pl

)

Experimental Section

j

∑(kh

nj,l

)1+(

j,lcD,j)

j

(6) np,l pl

j,lcD,j)

)

j

where Qi and QmaxH,l are the bound amount of i and the maximum amount of l-type sites for proton binding, respectively, both expressed in mol kg-1; kh i,l is the mean value of the lth affinity distribution, ni,l is the specific nonideality parameter seen by each particular ion i; pl is the generic heterogeneity parameter representative of the humic matter surface, and cD,i is the concentration in the model Donnan phase (eq 9). In potentiometric acid-base titrations, where essentially only protons are involved, the NICCA model becomes a bimodal Langmuir-Freundlich (L-F) isotherm, given by

QH ) QmaxH,1

(kh H,1cD,H)mH,1 1 + (kh H,1cD,H)mH,1

+

QmaxH,2

(kh H,2cD,H)mH,2 1 + (kh H,2cD,H)mH,2

(7)

where mH,l is the overall nonideality parameter for the lth kind of site seen by the proton, and it is related to the other parameters as mH,l ) nH,l pl. Therefore, metal ion binding data are needed to split the apparent heterogeneity into the generic and the intrinsic heterogeneities. The affinity distribution associated to each L-F isotherm has the shape of a Sips distribution (20), and it is given as a logarithmic representation for each lth kind of site 2

f(log k) )

{

QmaxH,l

∑Q l)1

×

maxH

}

ln(10)sin(πmH,l)

π[2cos(πmH,l) + 10mH,l(log k-logkh H,l) + 10mH,l(logkh H,l-log k)]

(8) where QmaxH ) QmaxH,1 + QmaxH,2. The Donnan model correction yields the concentration of each ion in the permeable gel phase, cD,i, which is calculated from the bulk concentration (c/i ) and the Boltzmann factor as

cD,i ) c/i exp

(

)

-ziFψD RT

(9)

where ψD is the Donnan potential (V), F is the Faraday constant (C mol-1), R is the gas constant (J mol-1 K-1), and T is the temperature (K). The Boltzmann factor is computed from the electroneutrality condition for a gel with a negative structural site density (18)

Q/VD +

∑z (c i

D,i

- c/i ) ) 0

to depend on the ionic strength only (18) and Q is the net charge of the fulvic substance. Although some authors have pointed out that the Donnan approximation seems unrealistic when applied to relatively small molecules such as fulvic acids, it has been widely used in the literature, and a discussion of the possible limitations of such approach is out of the scope of this work.

(10)

i

where VD is the Donnan volume (L kg-1), which is assumed

Reagents and Instrumentation. Succinic acid, Ba(OH)2, KNO3, KOH, and HNO3 were Merck analytical grade. KOH and HNO3 0.1 mol L-1 titrisols were used in the acid-base titrations. KNO3 was used as supporting inert electrolyte at 0.10 mol L-1. Metal ion solutions were prepared from 10-2 mol L-1 stock solutions, previously standardized by complexometric titration (21). Fluka supplied a fulvic acid commercial sample that was treated according to a procedure analogous to the one described elsewhere (22). The fulvic acid was dissolved in water and then diluted solutions of KOH and HNO3 were added in two steps with continuous stirring (24 h each). The resulting solution was centrifuged for 50 min at 12 000 rpm, and the solution was dialyzed (MWCO ) 3500 D). Finally, the solution was passed through a ionic exchange column (Bio Rad AG 50 W-X4) in order to obtain the fulvic acid protonated form. Such solution is considered the standard fulvic acid solution with a total organic carbon (TOC) of 1.79 g L-1. Potentiometric measurements were carried out with an Orion SA 720 pH-meter attached to a Metrohm 665 Dosimat, for the automatic addition of solutions, and to a personal computer through a RS232 card by means of a QBASIC data acquisition software package developed in our laboratory. The potentiometric cell outlet was connected to a saturated Ba(OH)2 solution in order to prevent CO2 entry. Voltammetric measurements were carried out with an Autolab System (Eco Chemie) attached to a Metrohm 663 VA Stand and to a personal computer by means of the GPES4 (Eco Chemie) software package. The system was also connected to a Metrohm 665 Dosimat, for the addition of titrating solutions, and to an Orion SA 720 pH-meter for monitoring the pH value during the experiments. In all cases the reference electrode, to which all potentials are referred, was Ag | AgCl | (3 mol L-1) KCl and the counter electrode was a glassy carbon electrode. Static mercury drop electrode (SMDE) and hanging mercury drop electrode (HMDE) were used as working electrodes. Glass cells (originally provided by Metrohm) were used in all voltammetric measurements because under the experimental conditions employed adsorption onto the cells wall is not significant (23). Ultrapure filtered water (Milli-Q plus 185 water purification system) was employed in all experiments, which were carried out at 25 ( 0.1 °C. Purified nitrogen was used for deaeration and blanketing of solutions. Procedure and Data Treatment. Potentiometric Titrations. The standard fulvic acid solution (15 mL) was extensively deaerated to completely remove the CO2 by bubbling purified nitrogen over and through the solution. Then, the exact amount of KNO3 to set the ionic strength (0.10 mol L-1) was added, and the nitrogen was passed only over the solution. The release of protons caused by the potassium ions is recorded as the initial charge of fulvic acid (Q0). Titrant additions were not done until the potentiometer readings were stable during several minutes. The electrode system was calibrated by the Gran method (24), in which a solution containing only the same salt level and some amount of a standard acid is titrated with the same standard base solution as in the sample titration. In this way, it is not necessary to take into account the activity coefficients, because the calibration is carried out under exactly the same conditions as for the sample. It also allows one to check the possible VOL. 35, NO. 6, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 1: Ligand Concentration Levels and Parameters Used in Voltammetric Titrations parameters  φex QmaxH/mol kg-1

Cd 0.005 0.59 0.039

Cu

0.39 0.098

0.005 0.43 0.012

0.30 0.030

Pb 0.005 0.43 0.024

0.35 0.039

TABLE 2: Parameters Obtained for Proton Binding (Acid-Base Potentiometric Titration) and Metal Ion Binding (Voltammetric Titrations) from the Fitting of the Coverage Data to Eqs 7 and 6, Respectivelya generic parameters

low affinity

high affinity

VD ) 2.5 L (18) QmaxH,l/mol kg-1 pl

3.33 ( 0.04 0.54 ( 0.01

1.59 ( 0.06 0.59 ( 0.01

kg-1

ion specific parameters log kh1/L mol-1 H Cd Cu Pb

3.68 ( 0.02 2.3 ( 0.2 4.2 ( 0.2 3.79 ( 0.01

FIGURE 2. Experimental acid-base potentiometric titration at KNO3 0.1 mol L-1 (O) and fitted (‚‚‚) proton binding curve vs p[H]D, and the corresponding affinity spectrum (s), both computed from the Table 1 values. p[H]D is calculated according to eq 9.

n1

log kh2/L mol-1

n2

0.76 ( 0.01 0.56 ( 0.02 0.54 ( 0.01 0.55 ( 0.01

8.27 ( 0.02 6.29 ( 0.05 8.7 ( 0.1 8.38 ( 0.01

0.95 ( 0.02 0.72 ( 0.01 0.66 ( 0.02 0.70 ( 0.01

a The confidence intervals are computed as usual in the case of samples with few points, except for the proton binding parameters, for which the confidence level was estimated from eq 7 fitting.

contamination of the solution titrated and the determination of the ionic product of water (Kw) at that salt level and temperature. Voltammetric Titrations. The succinic buffer solution (5 mmol L-1) containing a fixed KNO3 concentration (0.10 mol L-1) was placed into the voltammetric cell (25 mL). The presence of the buffer (pH ) 6) ensured a constant pH along the titration. Then, voltammograms were recorded to obtain the limiting current (I0lim) values in the absence of fulvic acid for several metal ion solution additions. After that, a straight line was fitted to the experimental I0lim vs cT,M* plot. Finally the same procedure was repeated, but a fixed amount of fulvic acid was added to the blank solution. To achieve the required ligand concentrations for each titration, suitable standard fulvic acid dilutions were made. All the ligand concentrations used for voltammetric titrations are gathered in Table 1. The measurements of such voltammograms yield a new set of current (Ilim) data, and φ values are computed (eq 3). Replicates of experiments at two different fulvic acid concentration levels were made for each metal ion. Then, it was possible to estimate the reproducibility between replicates and the reliability of the parameters between the two concentration levels. The errors were computed as it is usual in the case of samples with few points, i.e., computing the confidence range as the maximum minus the minimum value divided by two. The voltammograms were smoothed and measured by means of GPES4 software (Eco Chemie). Several homemade programs implemented in MATLAB (25) allowed the estimation of the c/M and c/ML values. TableCurve 2D software was used in the nonlinear fitting processes.

Results and Discussion Proton Binding Data - Potentiometric Protolytic Titration. The proton binding parameters (Table 2) were obtained as described in refs 18 and 26 and outlined in Figure 1. Figure 2 shows Q as a function of pHD, for the fulvic acid at a fixed value of ionic strength, and the fitted isotherm from eq 7. The value of pHD, which is the pH in the Donnan phase, is calculated according to eq 9. Figure 2 also shows the affinity 1100

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FIGURE 3. Cottrell plots for RPP limiting currents for Pb FA system at different values of the pulse duration, tm, for the following c/T,L/ / cT,M ratios: 0 (0), 1.8 (]), 6.6 (4), 15.3 (×), 30.4 (f), and 92.7 (O). spectrum associated with such potentiometric titration data by using eq 8. Two parameters are necessary to proceed with the calculations: Q0 and the Donnan volume, VD. Q0 was computed from the experimental curve (Q0 ) 0.52 mol kg-1) as explained in potentiometric titrations section, and VD was put equal to the value obtained by Benedetti et al. in ref 18 (2.5 L kg-1). The Donnan volume was fixed, rather than estimated from the master curve method, because a similar fulvic acid has already been described in the literature under the same experimental conditions. The proton binding values (Table 2) agree with those for other humic matter, taking into account the differences in their origins (18, 19) and the polyelectrolytic corrections used, either via Donnan (18, 19) or via Poisson-Boltzmann (27) approaches. Voltammetric Characterization of the System. Previous to the voltammetric titrations, some experiments involving Cd, Cu, and Pb solutions were carried out in order to check the behavior of the systems, without and with fulvic acid. The electrochemical lability of all the metal-fulvic acid systems was confirmed through the cathodic shift of the halfwave potential values with an increasing fulvic acid concentration. Moreover, the Cottrell plots (Figure 3) confirm a linear relation of the limiting currents with tm-1/2 (tm being the time window for the voltammetric technique) with an intercept very close to zero (30). Slight distortions in some voltammograms might be related to the double layer behavior of the fulvic acid or to loss of electrochemical reversibility of the metal ion reduction process. They involved a decrease in the slope of the RPP waves, expressed through RΤ, and an increase of the separation between the cathodic and anodic peak potentials, (Ecp - Eap), for cyclic voltammetry (CV). For the Cd + FA system, it can be seen that neither loss of reversibility nor

FIGURE 4. Average O experimental values from voltammetric titrations of fulvic acid at KNO3 0.1 mol L-1 in a succinic 5 mmol L-1 buffer and the corresponding errors in a secondary axis (]) and (+) for Cd, (O) and (×) for Pb, and (0) and (s) for Cu. QmaxH was 0.039 mol kg-1 for Cd and Pb and 0.012 mol kg-1 for Cu. The arrows mark the O ex value found by extrapolation from the curve. heterogeneity significantly influences on the signal. The Pb + FA system exhibited slightly distorted waves, but from the CV measurements and the application of the corresponding reversibility tests (29), it can be concluded that the elongations are mainly due to the heterogeneity (11). Finally, the RPP distortions are the strongest for the Cu + FA, both in RT and (Ecp - Eap) values; therefore, loss of reversibility and/or heterogeneity effects appear to be important (11). Anyway, the application of the present voltammetric procedure is not restricted by loss of reversibility, since only limiting currents are considered. Moreover, the use of RPP limiting currents minimizes the influence of electrodic adsorption (30). A large excess of ligand was added to ensure φ attaining a limiting value; in these conditions φ tends to 1/2 and then  can be estimated (“voltammetry” box in Figure 1). The computed value is 0.005 (Table 1), which is in good agreement with other voltammetric determinations (31). Metal Ion Binding - Voltammetric Titrations. In Figure 4 one of the averaged φ vs log cT,M* curves for several voltammetric titrations carried out at two ligand concentrations (Table 1) are shown for Cd, Pb, and Cu. The errors are displayed in the secondary y-axis. All the curves attain a plateau for excess ligand conditions, i.e., at low metal concentrations, and the value of φex is calculated by extrapolating the experimental φ values (“voltammetry” box in Figure 1). The voltammetric titrations were carried out in a buffered succinic medium to prevent changes in the pH along the titration. Hence, kh i,l values must be corrected from the metal ions binding to succinic buffer by the side-reaction coefficients. For each metal ion, the dilution of the fulvic acid was fixed such that 0.75 > φex > 1/2, because this is the most sensitive range to study the metal ion binding by voltammetric techniques. Moreover, the ligand concentration values chosen had the same levels as those typically occurring in natural samples, so the extrapolation to natural conditions would be more significant. Table 1 collects all the φex, , and QmaxH values corresponding to each metal ion titration. Then, following the scheme outlined in Figure 1 and in the theoretical section, these values are used in order to compute the binding curve through solution of eq 4 and then by fitting the binding curve to the NICCA-Donnan model (Table 2). In Figure 5 the experimental and the fitted binding curves are shown for Cd, Pb, and Cu at one of the FA concentrations for the sake of clarity. The fittings are good for metal loadings higher than 2.5 × 10-4 mol kg-1. For lower metal loadings, the experimental data deviate from the fitted curve, which can be due to several reasons. One likely explanation could be the reported limitations of the Langmuir-Freundlich

FIGURE 5. Experimental (open symbols) and fitted (solid lines) binding curves (mol of M/kg-1 of fulvic acid) corresponding to the complexation of Cd (]), (0), and (+), Pb (O) and (/), and Cu (×) and (4) by fulvic. They are derived from the voltammetric titrations shown in Figure 4. isotherm when the degree of coverage tends to very low values, which is our case (coverage should be linear with cM). Moreover, only data corresponding to the range φex < φ < 1 contain useful information about the complexation model, thus determining the experimental window of concentrations or affinities checked (when φ reaches φex value only the mean affinity is relevant). Finally, the experimental data deviation range is close to the detection limit of the RPP technique; therefore, a greater error is associated with such experimental data, and it could be another likely cause for the observed deviations. The values obtained for the binding of Cd, Pb, and Cu by fulvic acid are given in Table 2, which deserve several comments: (i) We have found a number of low-affinity sites which is roughly two times the number of high-affinity sites. The fact that ni,1 is lower than ni,2 is consistent since a rise in the density of one kind of sites will increase the interactions between metals on such kind of sites leading to a less ideal binding (lower ni,l values). (ii) For each kind of sites nH,l displays the highest value compared to that of metal ions, thus indicating that interactions, stoichiometric effects, etc., have the lowest influence for proton binding as it is expected from the charge and size of such ion. (iii) Some analogies can be noticed with results reported in the literature (19). For instance, the values obtained for the binding of Cd, Pb, and Cu by fulvic acid for the higher affinity sites (log kh i,2 column in Table 2) show the same sequence Cd < Pb < Cu ≈ H (13, 17, 19). The main differences with the cited studies refer to the heterogeneity factors. In the present work ni,1< ni,2 for all metals, which is not the case in ref 19. It could be due to structural differences among humic matter from various origins, which is not completely removed by the homogenization process performed in that kind of studies (22). The kh i,l values appear to be more insensitive to those structural differences, because the groups involved in the binding have similar identities (carboxylic or phenolic). This reasoning was also used in ref 13 to explain the results for humic matter from diverse origins. However, the kh i,l values for metal ions gathered in Table 2 are systematically higher than the ones reported in the literature. This could be due to the fact that the present RPP working range is mainly focused to lower metal loadings as compared to those previously reported (13, 17, 19). Hence, with respect to the affinity values involved in the metal binding, the sites with higher affinities should be more important, shifting the distribution toward higher kh i,l values. From the above discussion, it can be concluded that the method summarized in Figure 1 provides satisfactory results VOL. 35, NO. 6, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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for the metal ion-fulvic acid interactions within the concentration range of organic matter in natural samples. Thus, the DOC levels used in the present study (4-18 mg L-1 range, except one sample at 36 mg L-1, Table 1) are comprised in the usual ranges 1-20 and 0.25-3 mg L-1 for fresh- and surface seawater, respectively (see p 24 in ref 3). Further studies should be focused to extend the present voltammetric methodology in the application of stripping techniques that, despite being more involved from the electrochemical point of view, provide the very low detection limits required for metal ion speciation analysis.

Acknowledgments The authors gratefully acknowledge the financial support from the Spanish Ministry of Education and Culture (Project PB96-0379) and from the Generalitat de Catalunya (Projects SGR97-385 and SGR97-264 and FI grant for F. Berbel); Miguel Angel Benade for the fulvic acid purification and preparation; and Dr. Albert Sorribas (Lleida University) for the Table Curve 2D campus license. Last but not least, helpful discussions with Dr. Herman P. van Leeuwen (University of Wageningen), Iberdrola Visiting Professor in Barcelona and Lleida, are also acknowledged.

Nomenclature R

polynomial parameter, eq 5a

RT

parameter calculated from the RPP wave slope

β

polynomial parameter, eq 5b

c/i

bulk concentration of the formal species i

γ

polynomial parameter, eq 5c

Di

diffusion coefficient of species i

Ecp, Eap

cathodic and anodic peak potential for cyclic voltammetry, respectively



diffusion coefficient ratio:  ) DML/DM

φ

normalized limiting current, eq 3

Ilim

limiting current for RP polarograms

I0lim

limiting current for RP polarograms in absence of fulvic acid

Kc

average stability constant, eq 1

kh i,l

mean affinity constant for species i and of lth kind of site

Kw

ionic product of water

mH,l

overall nonideality parameter for proton and of lth kind of site

ni,l

specific nonideality parameter for species i and of lth kind of site

p[H]D

p[H] values corrected for polyelectrolytic effects

pl

generic heterogeneity parameter for lth kind of site

Q

net charge of the fulvic substance

Q0

initial charge density of the fulvic acid

Qi

fulvic acid site density in mol kg-1 for species i

QmaxH

maximum site amount for proton binding (QmaxH is proportional to c/T,L)

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tm

time window of the voltammetric technique

VD

Donnan volume of the fulvic acid in L kg-1

Y

measure of bound metal ion, Y ) cML/cT,M

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Received for review May 25, 2000. Revised manuscript received November 20, 2000. Accepted December 11, 2000. ES000111Y