Environ. Sci. Technol. 2008, 42, 9289–9295
The new electroanalytical technique AGNES (Absence of Gradients and Nernstian Equilibrium Stripping) has been applied to follow Pb2+ complexation to Purified Aldrich Humic Acid. A refined methodology of AGNES, allowing considerably larger gains, reached free metal ion concentrations down to subnanomolar values in a reasonable deposition time due to the lability and mobility of these complexes. Further insights into the meaning of the binding data, fitted to a NICA (Non Ideal Competitive Adsorption) isotherm, can be obtained with the concept of conditional affinity spectrum (CAS). For this purpose, we present the analytical expression for the CAS of NICA isotherm and show the CAS distributions for the Pb binding at fixed pH. Results reveal that the underlying spectra of each elementary distribution of the bimodal NICA evolve with pH yielding different overlapping and nonsymmetrical distributions. A non-negligible occupation of phenolic and carboxylic sites by Pb2+ takes place in the range of 4 < pH < 9.
justify NOM binding data via the distribution, either continuous or discrete, of sites with different affinities. This distribution is known as the affinity spectrum. In this approach, the global coverage is seen as a weighted sum of coverages of sets of sites with common affinity. In the simplest version, the coverage dependence (with free metal ion concentration) for each set is described by a Langmuirian isotherm. The calculation of the affinity spectrum (i.e., the inversion of a given isotherm or coverage data) has been tackled with analytical approaches (e.g., the inversion of Langmuir-Freundlich by Sips (4)), or with numerical techniques based on regularization methods (5). For systems with competing cations, the affinity spectrum becomes multidimensional. However, there are important limitations to its straightforward application. For instance, the concept of multidimensional affinity spectrum cannot be used when metal and proton do not share the same complexation sites (as in the case of chelate complexation). A less restrictive formalism relies on the concept of conditional affinity spectrum (CAS) (6). CAS is always monodimensional and characterizes the affinity distribution for a given ion while fixing the concentrations of all other ions. The experimental approach to complexation description requires data of free and bound metal. AGNES (Absence of Gradients and Nernstian Equilibrium Stripping) is a stripping electrochemical technique specifically designed to probe free metal ion concentrations (7), which has already been used for determining free Zn concentration in Mediterranean seawater (8) and in studying the complexation of heavy metals to humic acid (HA) (9). However, the attainment of low free concentrations with the standard application of AGNES could require prohibitively long times. A first aim of this work is the theoretical founding and experimental testing (via comparison with ion selective electrode measurements) of a novel strategy to reach lower free Pb concentrations in its complexation with purified Aldrich humic acid (as representative of NOM behavior for the methodological purposes of this work). These data will be used for the main objective of this work: the interpretation of Pb-HA complexation in terms of the conditional affinity spectra of the bimodal NICA isotherm, exploiting the analytical expression here derived for the first time.
Introduction
Principles of AGNES and a New Strategy to Reduce Deposition Time
Conditional Affinity Spectra of Pb2+-Humic Acid Complexation from Data Obtained with AGNES J A U M E P U Y , † J O S E P G A L C E R A N , * ,† ´ SAR HUIDOBRO,† CE ´ COMPANYS,† ENCARNACIO ´ R I A S A M P E R , † J O S E P L L U ´I S G A R C E ´ S,† NU ‡ AND FRANCESC MAS 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), Universitat de Barcelona, Martí i ´ 1, 08028 Barcelona, Spain Franques
Received July 29, 2008. Revised manuscript received September 17, 2008. Accepted September 24, 2008.
The circulation and the toxic or nutritional impact of a trace metal in the environment are strongly dependent on its complexation with natural organic matter (NOM) present in the aquatic media and soils, because the distribution among species affects the (bio)availability of the element (1). So, novel methods to quantify the speciation and to reach a deeper understanding of the characteristics of such complexation are of interest. Given that NOM is a mixture of a large number of different molecules, complexation with NOM is heterogeneous (2), not only because of the different functional groups, but also due to the interactions of the group with different chemical environments. On the other hand, there is a competition between proton and metal forsat leastssome of the sites. These issues are addressed by advanced isotherms such as NICA (nonideal competitive adsorption) isotherm (3). Alternatively to a description by isotherms, it proves useful to * Corresponding author e-mail:
[email protected]. † Universitat de Lleida. ‡ Universitat de Barcelona. 10.1021/es8021123 CCC: $40.75
Published on Web 11/14/2008
2008 American Chemical Society
We summarize the general principles of AGNES and specific information relevant for the enhanced methodology developed here (particularized to the case of Pb, although it applies to other amalgamating metals), while further details can be found elsewhere (7-12). AGNES provides a robust measurement of the free Pb concentration in solution, cPb, via two conceptual stages: deposition (preconcentration of the metal of interest by reduction and amalgamation in a hanging mercury drop electrode) and stripping. We define the gain, Y, for a given applied potential, E, as the preconcentration factor associated to Nernstian equilibrium: Y)
cPb 2F ) exp - (E - E0) cPb0 RT
[
]
(1)
where cPb0 is the amalgamated Pb0 concentration at the electrode surface, F is the Faraday, R is the gas constant, T is the temperature, and E0′ stands for the standard formal potential of the redox couple Pb2+/Pb0. The aim of the first stage is to preconcentrate Pb0 in the amalgam, until diffusive and Nernstian equilibrium up to a VOL. 42, NO. 24, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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prescribed gain Y. To optimize the deposition time, this first stage can be split into two substages: (a) in the first one, for a time t1,a, we apply E1,a corresponding to diffusion limited conditions (e.g., a practically unattainable Y1,a ) 1010) and (b) in the second one, for a time t1,b, we fine-tune the desired gain Y1,b ) Y applying E1,b. If the first stage is too long, an excess of Pb0 (with respect to the desired value Y × cPb) can be accumulated inside the drop, producing an “overshoot” at the switching from E1,a to E1,b, which produces a reoxidation current (on top of the residual steady-state current mostly due to the reduction of traces of dissolved oxygen), as seen in Figure S1 of the Supporting Information. It was shown (10) that a t1,b ) 3 × t1,a was a safe combination for the overshoot to be compensated up to 1% accuracy. The aim of the second stage is to quantify the accumulated Pb0 concentration. If we apply a potential step E2 under diffusion limited conditions for reoxidation, the measured current is proportional to the amalgamated concentration which is Y × cPb, resulting in the fundamental relationship of AGNES: ∗ I ) hcM
(2)
where I is the faradaic current (once an adequate blank has been subtracted) and h is the proportionality constant. This mode of operation avoids usual complications in voltammetry such as electrodic adsorption, variable hydrodynamics regimes, variable solution dynamics, etc. The practical implementation of AGNES with the hanging mercury drop electrode has required, up to date, moderate gains (say Y ≈ 100 (7, 9, 10) or Y ≈ 500 (8, 11). The probing of subnanomolar concentrations for environmentally relevant studies demands larger Y without a direct proportional increase in the deposition time. With this aim in mind, we explore the possibility of reducing the ratio between the second and first substage times to just t1,b ) t1,a exploiting the simple model (based on excess of ligand conditions) from ref 10. As detailed in the Supporting Information, we reach: I(χ) ) 1 + (χ - 1)e-χ hcPb
(3)
where χ is a dimensionless time, quotient of t1,a over a characteristic accumulation time depending on the diffusion coefficients of the mixture, lability characteristics, etc., and h × cPb is the exact AGNES current eventually attained. When χ ) 1, there is no overshoot nor undershoot: AGNES conditions have been exactly fulfilled at the end of the first substage. A simple analysis (see SI) allows the conclusion that, when the model is valid, once an overshoot is produced (χ > 1), the maximum possible error is 13%, which seems acceptable for most practical purposes. From this theoretical consideration, when the proportion t1,b ) 3 × t1,a is too prohibitive in time requirement, we can follow a new strategy: if we see the appearance of overshoot in the first stage (and we can accept excess of ligand conditions), then we just take t1,b ) t1,a.
Experimental Section Instrumentation and Reagents. Voltammetric measurements were carried out with an Eco Chemie Autolab PGSTAT30 potentiostat attached to a Metrohm 663VA Stand being controlled from a computer by means of the GPES (Eco Chemie) software package. The working electrode was a Metrohm multimode mercury drop electrode. The smallest drop in our stand was chosen, which according to the catalogue corresponds to a radius around r0 ) 1.41 × 10-4 m. The auxiliary electrode was a glassy carbon electrode and the reference electrode was Ag/AgCl/3 mol L-1 KCl, with a 0.1 mol L-1 KNO3 jacket (Metrohm 6.0726.100). 9290
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The solution was stirred with the PTFE tip stirrer of the Metrohm 663VA Stand. The rotation rate was fixed at 1500 rpm for all experiments. pH was monitored with a glass combined electrode (Orion 9103) attached to an Orion Research 720A ion analyzer. Free Pb2+ concentrations in solution were also measured potentiometrically using a Pb ion-selective electrode (Metrohm 6.0502.170) and the same reference electrode of Ag/ AgCl/3 mol L-1 KCl, with a 0.1 mol L-1 KNO3 jacket (Metrohm 6.0726.100), as used for voltammetry, both connected to the Orion Research 720A ion analyzer. Routine calibrations were performed with total Pb concentrations ranging from 1 × 10-6 M to 5 × 10-4 M in 0.1 M KNO3. Proton titrations were performed with a homemade program that controlled both a pH-meter 920A (Orion Research) and a digital burette Dosimat 665 (Metrohm). A separate pH electrode (Metrohm 6.0133.100) and an Ag/ AgCl/3 mol L-1 KCl reference electrode with a 0.1 mol L-1 KNO3 jacket (Metrohm 6.0726.100) were used to measure the pH. A magnetic stirrer MR3001K (Heidolph) was used to stir the solution and N2 was bubbled to deaerate. A glass jacketed cell provided by Metrohm, thermostatted at 25.0 °C, was used in all measurements. Humic acid (H1, 675-2; Aldrich) was purified with the procedure outlined elsewhere (9). Lead stock solutions were prepared from a 1000 ppm standard solution (Merck). Potassium nitrate was used as the inert supporting electrolyte and prepared from solid KNO3 (Merck, Suprapur). KOH and HNO3 titrisol (Merck) were added to fix the pH to the desired values. Ultrapure water (Milli-Q plus 185 System, Millipore) was employed in all the experiments. Purified water-saturated nitrogen N2(50) was used for deaeration and blanketing of solutions. Methods. Proton titrations were performed with a solution containing initially 0.5 g L-1 of HA in 0.1 M KNO3 after pH was increased up to 7.0 and back to pH 3.5 to avoid hysteretic effects (13, 14). Then the solution was titrated to pH 10.0 with KOH. After each addition the potential was read with a drift criterion of 0.1 mV min-1. The pH electrode was previously calibrated following Gran’s method, i.e., titrating a solution of HNO3 and KNO3 0.1 M with KOH 0.1 M (15). Metal titrations were performed at fixed pH (4, 5, 6, 7, 8 and 9) for an initial HA concentration cHA ) 0.45 g L-1 in KNO3 0.1 M as background electrolyte. The first value of Y (at the lowest total Pb concentration, cT,Pb) was adjusted to yield a current above the limit of detection. The times for the standard two-substages strategy (10) are t1,a ) 35 s and t1,b ) 3 × t1,a for Y ) 50; larger Y would, in principle, require proportionally larger times (e.g., t1,a )3500 s for Y ) 5000), but were dealt here with the new strategy t1,b ) t1,a with checking of overshoot. After some metal additions, the value of Y could be progressively reduced as the cPb increased, thus reducing the deposition times. For smaller Y, the standard strategy was used. A detailed record of the gains and combinations of times applied can be seen in the SI. The relatively high HA and total metal concentrations used in the titrations facilitate the comparison with ISE for the methodological developments studied here. From the measurement of cPb along a titration of humic acid with increasing amounts of total Pb, the total (specifically and electrostatically) bound Pb, QPb can be computed (9, 13) as QPb )
(cT,Pb - cPb)1000 cHA
(4)
Pb Binding to Humic Acid NICA isotherm has been widely used in the description of ion binding to heterogeneous organic matter. Sometimes
the binding energy is split into an electrostatic component and a chemical or intrinsic one by using some polyelectrolytic treatment. To have more direct values of the total energy of binding experienced by a cation under some conditions and to avoid numerical artifacts associated with the modeling of the electrostatic contribution, we will here analyze the raw binding data. The resulting NICA parameters will then be conditional to the ionic strength of the medium. For a monomodal distribution with index j (where index j ) 1 can be roughly thought as mainly associated with “carboxylic sites” and j ) 2 to “phenolic sites”, both distributions affected by the electrostatic contribution), taking into account competition between H+ and Pb2+, NICA isotherm reads
conditional affinity spectrum (CAS) (6) can be very useful. Indeed, by fixing cH, the bicomponent isotherm becomes monocomponent and the affinity spectrum becomes monodimensional:
θPb,j(cH, cPb) )
where the prime denotes its conditional nature. The key point is that the existence of the CAS p(log k′Pb;c H ) cnt) is less restrictive than the existence of the multidimensional affinity spectrum. CAS is only restricted to the existence of the affinity spectrum underlying the resulting monocomponent isotherm at a fixed pH. The following inversion formula (20) can be used:
((kj H,jcH)
(kj Pb,jcPb)
nPb,j
(kj H,jcH)
nH,j
+ (kj Pb,jcPb)
nPb,j
nH,j
1 + ((kj H,jcH)
+ (kj Pb,jcPb)
nH,j
nPb,j pj
+ (kj Pb,jcPb)
)
nPb,j pj
)
(5)
cH is the proton concentration, nX,j (0 < nX,j e1) can be seen as representing the nonideality specific and/or the stoichiometric factor of each ion X (13, 16, 17) and pj (0 < pj e1) takes into account the generic heterogeneity of the macromolecule. kj H,j and kj Pb,j are parameters of this isotherm quantifying a sort of average affinity of the components. The coverage used in eq 5 is defined as QPb,j QPb,j ) θPb,j(cH, cPb) ) Qmax,Pb,j nPb,j Q nH,j max,j
(6)
QPb(cH, cPb) )
∑ j)1
1 + ((kj H,jcH)nH,j + (kj Pb,jcPb)nPb,j)pj
∫
∞
-∞
θPb(cH, cPb) )
∫ ∫ -∞
-∞
(7)
1 + 10logkHcH + 10logkPbcPb
1 + kPb cPb
d log kPb (9)
ln(10) )]| |Im[θPb(cH ) cnt, cPb ) -1 ⁄ kPb π (10)
where Im means “take the imaginary part”. Following this procedure (see SI for details), we derive the CAS for the bimodal NICA isotherm to be ln(10) × π
(
2
∑ j)1
nPb,j Q nPb,j pj-1 nH,j max,j (kj Pb,j ⁄ kPb ) Mj × 2p nPb,2 nPb,1 1 + Mj j + 2Mpj jcos(pjφj) Qmax,1 + Qmax,2 nH,1 nH,2
)
where 2nPb,j Mj(cH, kPb ) ) [(kj H,jcH)2nH,j + (kj Pb,j ⁄ kPb ) +
nPb,j ) cos(πnPb,j)]1⁄2 (12) 2(kj H,jcH)nH,j(kj Pb,j ⁄ kPb
p(log kH, log kPb) ×
10logkPbcPb
kPb cPb
[sin(πnPb,j - (1 - pj)φj) + Mpj jsin(πnPb,j - φj)] (11)
The coverage can be thought of as resulting from the superposition of coverages of a distribution of independent sites with varying intrinsic affinities (kH and kPb) for the binding cations. This distribution, denoted p(log kH, log kPb), is the (bidimensional) affinity spectrum providing the abundances of sites for a given combination of affinities (18). In the particular case dealt with here, with a Langmuirian local isotherm, the affinity spectrum, if exists, follows from the implicit equation ∞
p(log kH, log kPb)×
p(log kPb ;cH ) cnt)
;cH ) cnt) ) p(log kPb
Conditional Affinity Spectra
∞
∞
-∞
kPb c 1 + kHcH Pb d log kH d log kPb ) kPb 1 + kHcH + c 1 + kHcH 1 + kHcH Pb
(kj Pb,jcPb)nPb,j nPb,j Qmax ,j × nH,j (kj H,jcH)nH,j + (kj Pb,jcPb)nPb,j ((kj H,jcH)nH,j + (kj Pb,jcPb)nPb,j)pj
∞
-∞
p(log kPb ;cH ) cnt) )
where Qmax,j represents the number of moles of sites (in mol kg-1) for H associated to each distribution, Qmax,Pb,j is the maximum number of moles of Pb which can be bound, and Qmax,Pb,j ) (nPb,j/nH,j)Qmax,j due to the thermodynamic consistency relationship (13). With this normalization, θPb,j(cH,cPb) can reach a maximum value of 1. The bimodal NICA isotherm can, then, be written 2
∫ ∫
θPb(cH ) cnt, cPb) )
and cos(φj) )
(13)
To concisely characterize the distribution of a given CAS, we use the mean (first central moment) 〈log kPb 〉)
∫
∞
-∞
log kPb p(log kPb ;cH ) cnt)dlog kPb (14)
the variance (second central moment)
× dlog kH d log kPb (8)
Recent work (19) has developed a method to retrieve multidimensional spectra from analytical isotherms (e.g., the affinity spectrum associated to NICA when nH ) nPb), while pointing out that not all isotherms can be inverted. Of relevance here is the result that NICA isotherm has no bidimensional associated spectrum when nH * nPb. To overcome this (and other difficulties), the concept of
nPb,j (kj H,jcH)nH,j(kj Pb,j ⁄ kPb ) cos(πnPb,j) Mj
2 2 2 σPb 〉 ) 〈log kPb 〉 - 〈log kPb
(15)
with 2 〈log kPb 〉)
∫
∞
-∞
2 p(log kPb ;cH ) cnt)dlog kPb (16) log kPb
and the third dimensionless (or standardized) central moment (indicating skewness, a measure of asymmetry of the distribution) VOL. 42, NO. 24, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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3 ) aPb
1 3 σPb
∫ (log k
Pb -
< log kPb >)3dlog kPb
(17)
Results and Discussion Speciation and Coverage Data. NICA Isotherm. Proton titrations of HA were fitted to a bimodal NICA isotherm for just proton (i.e., taking cPb ) 0 in eq 7 and omitting the terms nPb,j/nH,j). In this case, the product nH,j pj is usually called mH, j. The retrieved fitting parameters can be seen in Table 1. The proton binding results can be described in terms of the proton affinity spectrum. For one ion, a monomodal NICA isotherm reduces to the Langmuir-Freundlich one, so the corresponding proton affinity spectrum is a bimodal Sips distribution. The upper thick continuous line in Figure 1 depicts this distribution resulting from the addition of a carboxylic distribution centered at log (kj H,1/M-1) ) 4.31 and a broader phenolic distribution (lower m2-value as compared j H,1/M-1) ) 10.4. The figure also depicts to m1) centered at log (k in discontinuous lines the occupied (protonated) sites of each affinity value kH at different proton concentrations by computing p(logkH)(kHcH)/(1 + kHcH). For pH ) 7, a typical value of the natural waters, more details are reported in the inset of the figure. Few carboxylic sites are protonated (markers O), while there are still phenolic sites not protonated since markers (0) do not converge to the phenolic distribution (depicted in dotted line) in the range of low affinity values. AGNES and ISE free Pb concentrations for six titrations of HA with Pb at six different pH values are shown in Figure 2. The satisfactory general agreement between AGNES and ISE lends support to the validity of the new strategy t1,a) t1,b and confirms, once more, that AGNES avoids the usual interference of electrodic adsorption on voltammetric techniques (21, 22) and provides the free metal concentration through a very simple interpretation of the response current. Relatively small deviations appear in the lower cPb range, (probably below the LOD of ISE (23) given the relatively low cT,Pb), being the ISE value slightly higher than the one retrieved by AGNES. We highlight the achievement of huge Y values (relatively to the ones published up to date): for instance, the experiments whose first stage is plotted in Figure S1, used Y as high as 50000, reaching, in one case, a free concentration 35 pM. We can conclude, then, that the desired accumulation could be obtained in relatively short t1,a because of a huge proportion of complexed Pb over free Pb, being this complexed Pb species sufficiently labile and mobile (11). The refined AGNES methodology here suggested allows a reduction of 50% of the deposition time required in the standard application of 2 pulses. Figure 3 shows the expected tendencies of increasing coverage (computed from AGNES determinations) with increasing free Pb concentration or increasing pH. Continuous lines in Figure 3 stand for the fitted bimodal NICA isotherm (7) which reproduces well the experimental binding data depicted with markers. The fitting parameters gathered in Table 1 show higher log kj Pb,j and lower nPb,j-values than
previously reported (24-26). Since we are including the electrostatic binding, the effective affinity is increased, while the variation of the electrostatic contribution with coverage increases the effective heterogeneity. However, differences between the present data and other data reported in the literature can also be ascribed to the particular properties of the HA considered or to differences in the separation/ purification procedure. CAS Associated to NICA. By using the parameters from Table 1 in eq 11, we can compute the associated CAS of Pb-HA binding at each of the probed pH values. As shown in Figure 4, the CAS shows only one peak for all the pH values studied with a shoulder in the high affinity tail in the range 4 < pH < 7 and a long tail in the low affinity range for pH > 7. When pH increases, the CAS shifts toward higher conditional affinity values. To understand the origin of the shoulder and the differences between the CAS corresponding to the different pH values, Figure 5 shows, just for three pH values, the contribution of the “elementary” carboxylic and phenolic distributions including their weighting factor ((nPb,j)/(nH,j) Qmax,j)/((nPb,1)/(nH,1)Qmax,1 + (nPb,2)/(nH,2)Qmax,2). The first striking feature is the “inverted” order of the peaks at low pH values with respect to a first-glance naive expectation: the peak of the conditional phenolic distribution has less conditional affinity than the peak of the carboxylic distribution. Indeed, as seen in Table 1, the carboxylic distribution exhibits a NICA adsorption constant log (kj Pb,1/ M-1) ) 4.37 while the phenolic one is log (kj Pb,2/ M-1) ) 7.57. These isotherm parameters could mislead to predict smaller affinities for the conditional carboxylic distribution than for the phenolic one. However, Figure 5 indicates that at pH ) 5 the peak corresponding to the carboxylic distribution shows (slightly) higher affinity than the phenolic one. This behavior can be rationalized taking into account that the CAS is an “effective” or “apparent” affinity spectrum at a given cH. Thus, for low pH values, the phenolic sites are predominantly protonated and, then, the effective affinity toward Pb2+ is weak, because this affinity can be interpreted as the remaining binding energy once the expulsion energy of H+ is discounted. When pH increases, (i) the exchange work decreases and (ii) the electrostatic contribution to the Pb2+ binding increases, so that the effective Pb-affinity of both distributions increase. Thus, the carboxylic and phenolic distributions shift toward higher affinities (see Figure 5), but with the phenolic distribution moving a longer distance because (i) the energy to extract the protons of the phenolic sites is higher than the energy required for the carboxylic sites and (ii) the higher proton occupation of the phenolic sites in all the pH values of Figure 4 as Figure 1 indicates. The evolution of the different CAS with pH can be followed via their moments (see Table 2). The carboxylic average affinity clearly increases from pH 4 to 7 and remains practically stable for higher pH values, which can be rationalized as due to the full deprotonation of the carboxylic
TABLE 1. NICA Parameters Retrieved by Fitting Proton and Metal Titrations of Humic Acid parameters of proton titration Qmax,1 / mol kg-1
log (k¯H,1 / M-1)
m1
Qmax,2 / mol kg-1
log (k¯H,2 /M-1)
m2
3.14
4.31
0.38
4.46
10.4
0.16
parameters of AGNES data
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nPb,1
log (k¯Pb,1/ M-1)
nH,1
p1
nPb,2
log (k¯Pb,2/ M-1)
nH,2
P2
0.65
4.37
0.92
0.41
0.61
7.57
0.46
0.34
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FIGURE 1. Affinity spectrum (upper continuous line) for proton binding to HA determined from NICA isotherm with parameters given in Table 1 and density of occupied sites (discontinuous lines) by protons at different pH (indicated by numbers). Inset: Affinity spectrum at pH 7 (thin upper continuous line) together with their component carboxylic (left dashed line) and phenolic (right dashed line) distributions. Proton occupation (thick continuous line), proton occupation of carboxylic sites (marker O), and proton occupation of phenolic sites (marker 0).
FIGURE 3. Experimental bound metal, QPb (markers for different pH values as in Figure 2) and fitted curves with bimodal NICA isotherm, eq 7, using retrieved parameters in Table 1.
FIGURE 4. Conditional affinity spectra (relative abundance of sites vs dimensionless affinity log(k′Pb/M-1) of the set of sites) of bimodal NICA isotherm obtained from eq 11 with the fitted parameters in Table 1.
FIGURE 2. Free Pb2+ concentrations measured by AGNES along HA titrations at fixed pH. AGNES markers: circle (O), pH 4; square (0), pH 5; triangle (4), pH 6; diamond (]), pH 7; asterisk (*), pH 8; line (-), pH 9. [HA] ) 0.45 g L-1. ISE markers: (×) for even pH values and (+) for odd pH values. Ionic strength ) 0.1 M. sites reaching the maximum value for their affinity average which corresponds to the “pure” affinity of Pb2+ for these sites in the absence of protons and equals the value 4.37 ) log (kj Pb,1/ M-1) since at this high pH the carboxylic NICA isotherm becomes a Langmuir-Freundlich one. The average affinity of the phenolic distribution keeps increasing with increasing pH (in the probed experimental range), this indicating that at pH 9 there are proton phenolic sites being deprotonated when Pb ions bind to these sites, as also seen in our proton titrations. In agreement with the visual inspection of Figure 5, the values in Table 2 indicate that the phenolic distribution mean is lower than the carboxylic distribution mean for pH < 7 and this relationship reverses for higher pHs (when all sites are progressively deprotonated) in accordance with kj Pb,2 being greater than kj Pb,1 (see Table 1). The variance or second moment of the CAS is intuitively related to the width of the distribution and can be seen as an indicator of the degree of heterogeneity of the binding. The variance of the carboxylic distribution increases with pH, indicating that, when the carboxylic sites are deprotonated, the effective range of Pb affinities increases (i.e., there are more varied affinities for the binding of the Pb ions). As
FIGURE 5. Carboxylic (continuous line) and phenolic (dashed line) distributions within the global CAS for NICA isotherm for three selected pH values. Parameters from Table 1. we see in Figure 5 that the carboxylic distribution broadens toward the right with increasing pH (i.e., there is an increase of the abundances of sites with higher affinities for Pb2+), we conclude that the new sites, available because of deprotonation, generally exhibit also a high affinity for Pb2+, so that strong affinity sites for the proton tend to be strong affinity sites for Pb2+. The variance of the phenolic distribution (Table 2) follows a pattern similar to the carboxylic one, but it is not stabilized yet at pH ) 9 indicating again that protons are still bound to the HA at this pH. A closer inspection of the differences between the CAS corresponding to pH 7 and 5 in Figure 5 shows a decrease in the abundances of the higher affinity tail of the spectrum (6 < log k′Pb < 9) as well as an increase of abundance of the lower affinities in a range immediately below (4 < log k′Pb < VOL. 42, NO. 24, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 2. Moments of the Distributions of the CAS Associated to the NICA Isotherm with Parameters Shown in Previous Tables bimodal NICA (global) pH 4 5 6 7 8 9
carboxylic distribution
′ /M-1)〉 〈log(kPb
′2 σPb
3 aPb
2.62 3.30 3.90 4.39 4.81 5.19
1.95 2.48 2.88 3.46 4.31 5.14
-1.01 -1.02 -0.84 -0.91 -1.04 -1.03
〈log
′ 〉 kPb
3.03 3.69 4.09 4.27 4.34 4.37
phenolic distribution
′2 σPb
3 aPb
2.73 4.04 5.12 6.12 6.91 7.41
-1.31 -1.04 -0.61 -0.35 -0.22 -0.10
〈log
′ 〉 kPb
2.47 3.15 3.82 4.44 4.99 5.50
′2 σPb
aPb
3
1.57 1.82 2.01 2.44 3.18 3.93
-1.07 -1.34 -1.28 -1.44 -1.63 -1.59
The first moment has been computed with eq 14, the second moment was computed with eq 15, and the third dimensionless moment was computed with eq 17.
the phenolic sites is not negligible and, thus, both distributions play a relevant role in the binding of Pb ions to this HA.
Acknowledgments Experimental help from Aida Serra is acknowledged. This work was financially supported 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”.
Supporting Information Available Figure of deposition currents, modeling t1,a ) t1,b in AGNES, tables with gains and deposition times used, and the analytical expression for the CAS associated to bimodal NICA isotherm. This information is available free of charge via the Internet at http://pubs.acs.org.
Literature Cited
FIGURE 6. Occupation of HA sites by Pb for two Pb concentrations at pH 7. The thick continuous line corresponds to the CAS of the carboxylic (panel a) and phenolic (panel b) distributions. Dashed lines stand for the Pb occupied sites of the corresponding distribution at the free Pb concentration indicated by the arrow. 6). This deformation in the carboxylic distribution leads to the loss of symmetry as indicated by the progressively more negative skewness (longer tails in the lower affinity region) with decreasing pH values (Table 2) and it could lead to a shoulder in the distribution or to double peaked forms for the monomodal NICA isotherm, depending on correlation, see ref 27. The current description of Pb complexation with HA based on conditional affinity distributions can also be used to analyze where Pb ions bind for a given pH and Pb concentration. Panels a and b in Figure 6 show the occupation of the sites by Pb ions at two Pb concentrations in the range of those used in the HA titrations for pH 7. Due to the heterogeneity of the carboxylic sites, even at pH 7 we have a non-negligible amount of Pb bound to carboxylic sites that have higher affinity than the phenolic sites occupied by Pb. This trend is similar to that of other pH values (see Figure S3 for plots at pH 4). The main conclusion of these figures is that at all assayed pH-values the complexation of Pb2+ to 9294
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