Oligoelectrolyte model for cation binding by humic substances

Environ. Sci. Technol. 1992, 26, 284-294

Oligoelectrolyte Model for Cation Binding by Humic Substances Bettina M. Bartschat,+ Steven E. Cabaniss,' and Franqols M. M. Morel*,§ EAWAG, Uberlandstrasse 133, CH-8600 Dubendorf, Switzerland, Department of Chemistry, Kent State University, Kent, Ohio 44242, and Department of Civil Engineering, 48-425, Massachusetts Institute of Technology, Cambridge, Massachusetts 02 139

An oligoelectrolyte model of humic substances is developed to explain ionic strength effects on copper and hydrogen ion titrations. After discussing the relevance of various polyelectrolyte models to humic substances, we choose a model in which the molecules are represented as impenetrable spheres. The electrostatic effect is calculated using numerical solutions of the appropriate nonlinear Poisson-Boltzmann equation. Incorporation of available data on molecular weight distribution, size, and functional group content of humic substances reduces the number of arbitrary fitting parameters. A simple model, containing two copper binding sites and an additional acidic site, and two size classes of impenetrable spheres, can successfully explain pH and copper titration data. In particular, the model results demonstrate the importance of size heterogeneity as a means of explaining the relatively small effect of ionic strength on pH titrations as compared to copper titrations. This difference is not attributable to the difference in charge between H+ and Cu2+and suggests that an electrostatic model calibrated only on a pH titration cannot describe a copper titration or vice versa.

Introduction Humic substances abound in natural waters and may have significant effects on metal speciation and mobility, especially in waters with high levels of dissolved organic carbon (DOC). At present, our ability to predict these effeds using equilibrium models is quite limited. A simple approach is to describe humic substances as consisting of a few discrete ligands of defined concentrations and binding properties. Usually two or three binding sites are required to fit a given complexometric titration. However, the resulting set of equilibrium constants is found to depend on pH, ionic strength, and the presence of competing metals. No methods exist to extrapolate such conditional constants from one set of conditions to another. Some workers have placed a greater emphasis on the heterogeneity of sites expected in humic substances. They typically represent the spread in binding strengths by a Gaussian distribution of (log of) equilibrium constants (I). This approach may be more pleasing conceptually than the discrete site model, but the end result is similar: though a single titration can be described with a small number of fitting parameters, extrapolation from a given pH or ionic strength to another is still not possible (2). Instead of extracting conditional parameters from a single titration curve, one can of course simultaneously consider the results of multiple titrations under a range of conditions. Cabaniss and Shuman (3) used this idea to fit a series of copper-fulvate titrations carried out at different p H s (5.14-8.44) and total DOC levels, using five discrete ligands with various proton-exchange stoichiometries. A similar approach could be used to model data showing competition for sites among different metals ( 4 ) . A continuous distribution model, using one Gaussian distribution of binding strengths for hydrogen ions and one 'EAWAG. f Kent State University. 8 Massachusetts Institute of Technology. 284

Environ. Sci. Technol., Vol. 26, No. 2, 1992

for copper ions, was used by Grimm et al. (5) to model a set of three copper-fulvate titrations (pH 2.5-4.5). However, these are still only curve-fitting exercises, which are not based on fundamental physical-chemical properties of humates and which do not allow extrapolation. A different approach to modeling pH and ionic strength effects on metal binding is to consider an explicit Coulombic contribution to the binding strength, which arises from the large charge on a humic acid molecule. For example, Tipping and Hurley (6) used an empirical functional form to describe this contribution, while Ephraim and Marinsky (7) assumed a Donnan equilibrium between humic and aqueous "phases". The hope in this approach is that, by accounting explicitly for such Coulombic effects in humic polyelectrolytes, a true (i.e., invariant) set of chemical binding constants (discretely or continuously distributed) may be extracted from the data. These constants together with the explicit Coulombic term should then provide an accurate description of metal binding under all conditions. Here we follow this approach, attempting to capture in a simple thermodynamic model of humic acids as much structural information as possible, particularly molecular weights and their distributions as well as functional group concentrations and chemistries. The predictions of the resulting a priori models are then compared to experimental data to explore how well metal binding by humate can be explained as a simple compounding of chemical affinities and Coulombic effects. We examine, in particular, the ability of our model to account for three specific features of titrimetric data in humates: the "smeared" appearance of acid-base and metal titrations, the much larger effect of ionic strength on metal ion titrations than on acid-base titrations, and the very high affinity of humates for metal ions such as copper at high ligand to metal ratios. Our goal here is not to obtain exact fits to experimental data; rather we wish to explore how well a simple a priori thermodynamic model of humate binding may explain the major qualitative features of the available data and on this basis to gain insight into the physical-chemical nature of humate complexation and the parameters that control it. Independent experimental verification of some of the model's assumptions and predictions is discussed in a companion paper by Green et al. (8). As will be seen, we obtained a satisfactory model by taking into account the oligoelectrolytic character of humic acids (intermediate between simple ions and true polyelectrolytes) and representing the humate molecules as impenetrable charged spheres. While this work was in progress, two other research groups independently chose models that also combine these two features to describe the acid-base chemistry of humates (9, IO). However, because our focus is on metal rather than proton binding, we have been forced in addition to consider explicitly the distribution in the size of the humic molecules.

Theory Electrostatic models for small ion interactions with other small ions, polyelectrolytes, and charged surfaces in elec0013-936X/92/0926-0284$03.00/0

0 1992 American Chemical Soclety

trolyte solutions have been studied for many decades and give us a starting point for a humate complexation model. However, none of these models directly fits our needs. Aiken and Malcolm (11)have pointed out that the term “oligoelectrolyte”may be most appropriate for a fulvic acid molecule. With a number-average molecular weight of close to 1000 Da and a carboxylic acid content of roughly 6 mequiv/g, the “average” humate molecule has a charge near -6, falling outside the range of both Debye-Huckel and polyelectrolyte theories. Although Debye-Huckel theory could still be applicable if the charged sites of one molecule were separated far enough (more than 1Debye length) to be treated independently, a simple consideration of DOM size suggests that this requirement is unlikely to be met. At 0.01 M ionic strength in aqueous solution, the Debye length is over 30 A while the average fulvic acid diameter, estimated by Aiken et al. (11,12),is closer to 10 or 15 A. Furthermore, a significant fraction of the functional groups in a fulvate sample may be parts of molecules with molecular weights much higher than 1000. In a flow field-flow fractionation study, believed to be more accurate for determining molecular weight distributions than more commonly used chromatographic methods, Beckett et al. (13) found that typical fulvic acid samples with average molecular weights near 1000 Da also included a large fraction (10% or more by weight) of molecules in the 5000-10 000-Da size range. In humates, approximately 5-20% of the total mass consisted of molecules in the 10000-25 000-Da size range. If we assume that the concentration of functional groups per weight is constant over the range of molecular weights, 5-20% of the functional groups should then be part of these larger molecules. Although this fraction of functional groups may be safely ignored when pH titration data are modeled [as DeWit et al. (9) and Tipping et al. (IO)have done], we will see in the modeling section of this paper that it may dominate the binding of divalent metal ions. An ideal “oligoelectrolyte” model for humic substances should therefore be able to handle a size distribution of molecules ranging from those almost described by Debye-Huckel theory (2 C 6) to ones closer to true polyelectrolytes (2 > 60). The key variable for calculating the Coulombic effect on the energy of a reaction is the electrostatic potential \k, usually obtained as the solution of a Poisson-Boltzmann equation. This equation assumes that \k is created by a central charged region of interest (e.g., the polyion), and that the small, mobile ions in the solution arrange themselves according to this potential. The equation is composed of two parts, the Poisson equation relating potential to charge density and a Boltzmann distribution of co- and counterions in the potential field:

(d\k/dr)I,+

= -g/e

(2)

where (d\k/dr)lr=R is the potential gradient at the surface (Gauss’ law). In a two-phase model, po is equal to total charge divided by total volume in the polyion phase and zero in the bulk phase. The boundary condition becomes (d\k/dr)lr=o = 0 (3) where r = 0 is the center of the charged region. In both the one-phase and the two-phase models, the other boundary condition (if one assumes infinite dilution of the polyion) is that the potential disappears at large distances from the central charged region: lim \k = 0 (4) ?m

Once \k at the site of the reaction has been calculated, the Coulombic free energy change (and hence the electrostatic effect on the equilibrium constant of a reaction) is obtained as the electrostatic work required to bring the charge of the fixed site from -Qe to (2 - &)e. As discussed in the Appendix, itis also convenient to consider a “local” concentration [Mz+] of the reacting MZ+,either at the surface of an impenetrable region or within the penetrable phase, where

[ S I

(5) Although it is the basis for most currently used theories of electrostatics of ions in solution, the Poisson-Boltzmann equation is not without flaws. The first concerns the assumption that the distribution of the mobile ions can be described by a continuous function representing the ions not as point charges but as “smeared” regions of charge, and that the mobile ions’ only interactions with each other are Coulombic. LeBret and Zimm (14) have used Monte Carlo methods to demonstrate that substantial errors may arise when the local concentration of counterions is so large that nonCoulombic interactions can no longer be ignored, or when the size of the counterions is not small compared to geometrical parameters (such as the cylindrical radius) of the polyion. Another problem arises from the inadequacies of the Poisson-Boltzmann equation itself, which assumes that the potential of an average force (the \E of the Boltzmann relation) is the same as the average potential (the \k of the Poisson equation). Kirkwood (15) showed that this is a good approximation only when le\k//kTI > I)while in Manning’s model they partially neutralize the charge and only condense at all if the charge density exceeds a certain value. A model of this type combined with a number of proton and/or metal binding sites has been applied to humic substances by Ephraim and Marinsky (7). One disadvantage of this model is that there is no easy way to account for size distributions. One could assume that p o is some function of molecular weight, but this introduces another arbitrary parameter into our model, which we are trying to keep as simple and constrained by our knowledge of the problem as possible. Another disadvantage is that even if fulvic acids can be well described as a penetrable phase, the Donnan formulation of a two-phase model is inappropriate if the humic ”phase” has a small radius, as discussed below.

Spherical Models None of the limiting cases discussed above satisfy our initial requirements for an appropriate humate complexation model. The linearized models are not generally applicable to oligoelectrolytes (as discussed before), while the Gouy-Chapman, Donnan, and Manning models cannot handle size distributions. The geometries of infinite planes and cylinders do not seem reasonable descriptions of humic substances in any case. Our simplest option then is to consider nonlinear solutions to a spherical PoissonBoltzmann equation, with the sphere either penetrable or impenetrable to mobile ions. To handle size distributions, we can assume that the molecular weight of the molecule is proportional to the cube of its radius and that all size groups have the same number of charged sites per unit weight. Then, in the case of the penetrable sphere, the charge density po will not vary with size, while in the case of the impenetrable sphere, the surface charge density u will increase in direct proportion to the radius. These models require a minimum of size parameters: a molecular weight distribution such as the one measured by Beckett et al. (13), a charge per unit weight ratio (measured titrimetrically and spectroscopically by a number of researchers), and a parameter describing the relationship between radius and molecular weight (which requires knowing the radius associated with a particular molecular weight). Data relating an average radius, measured by small-angle X-ray scattering, to a numberaverage molecular weight (12) should give a reasonable estimate of the last parameter, since the more abundant smaller molecules should dominate both averages. Unfortunately, the nonlinear forms of eq 1for spherical geometry do not have analytical solutions and we must resort to numerical methods in both cases. The result of

T

Table I. Parameters a , b , and c Used To Fit the Numerical Solutions of the Poisson-Boltzmann Equation of an Impenetrable Sphere to the Functional Form Given by eq 12”

R, A 7.7 10.0

15.0 20.0 50.0 100

ionic strength, M

a

b

C

0.001 0.01 0.1 0.001 0.01 0.1 0.001 0.01 0.1 0.001 0.01 0.1 0.001 0.01 0.1 0.001 0.01 0.1

0.01866 0.1966 1.201 ; 0.03138 0.2523 1.410 0.04762 0.3214 1.426 0.07375 0.4862 2.173 0.1626 0.7735 2.873 0.2213 0.9359 3.184

1.737 1.549 1.457 1.616 1.499 1.416 1.568 1.474 1.459 1.480 1.352 1.298 1.327 1.248 1.224 1.267 1.205 1.197

5.782 6.403 7.890 4.596 5.098 6.413 3.104 3.625 4.965 2.375 2.749 3.511 1.029 1.209 1.577 0.5495 0.6360 0.8730

5

2 0 1

0

20

30

40

50

60

70

80

90

100

Radius (A)

Flgure 1. Electrostatic factor log k of an impenetrable sphere as a functlon of radius and ionic strength. It is assumed that total charge is proportional to R 3 , so that the charge density u is Increasing proportionally to R. A charge density of 9.2 pC/cm2 was chosen for a radius of 7.7 A, consistent with the measurements of fulvlc acid molecular weight, size, and charge by Aiken et ai. ( 12) and Bowles et ai.

(30). 6

” Numerical calculations of log X do not deviate from the values

niven bv the functional form bv more than 0.01 loe unit (27).

5

a numerical solution is \k as a function of r (the distance from the center of the sphere) for a given ionic strength I , molecular radius R, and charge on the molecule. In the case of the impenetrable sphere, the relevant charge parameter is u, the surface charge density on the sphere (assumed to be uniform). Our calculations are described in Barbchat (27);other numerical solutions (agreeing with ours but not tabulated in a convenient form) have been calculated by Muller (28),Wall and Berkowitz (29),and DeWit et al. (9). The electrostatic factor X is analogous to that used in the Donnan model (eq 7) and is given by X = exp[-(e\ko/kT)]

10

(9)

where \k0 is the value of \k at the surface of the sphere. Since a functional form A vs u is needed to carry out equilibrium calculations, we have fit the results of our numerical calculations at each radius and ionic strength to a three-parameter function (Table I): u = a sinh ( b log A) + c (log A) (10) As also noted by DeWit et al. (9),the numerical solution approaches a linear form (the solution of the DebyeHuckel approximation) for small particles, and the Gouy-Chapman solution for large ones. The former is achieved when log A < 1,the latter when the curvature of ~ eq the molecule is larger than the Debye length, 1 / from 6, or 10, 32, and 100 A for ionic strengths 0.1, 0.01, and 0.001 M, respectively. We now assume that the acid content of a fulvic acid is 6.1 mequiv/g (30),and that an average molecule has a radius of gyration of 7.7 A and an average molecular mass of 711 Da (12). The total charge on the molecule of radius 7.7 8, is 4.3, leading to a u of 9.2 pC/cm2. Assuming that the molecular weight (and hence the total charge) is proportional to the cube of the radius, we can calculate u for other sizes, and obtain Figure 1, which describes the effect of size on A. It is important to note that, in all of the results shown here, the variable I refers to the concentration of monovalent ions only. The traditional definition of ionic strength is only useful when the Poisson-Boltzmann equation is linear, as in the Debye-Huckel model. In a nonlinear model, the presence of multivalent counterions

I

1+

-0

10

20

30

40

50

60

70

80

90

100

Radius (A)

Flgure 2. Electrostatic factor log k of a penetrable sphere as a function of radius R and ionic strength I. Dashed lines represent the “Donnan” llmit (electroneutrallty in the charged phase). Since total charge is assumed proportional to R 3 ,the charge density p o is not a function of radius. A value of 3.7 M was chosen, again consistent with measurements of fulvic acid molecular weight, size and charge by Aiken et ai. (72) and Bowles et al. (30).

will only be insignificant if XT >> ZLXq[Mz+](see eq 7). For example, for a value of A of 100 and a concentration of a monovalent salt of 0.01 M, a Ca2+concentration of M is sufficient to significantly affect the electrostatics of the system even though the ionic strength only changes by a few percent. In some freshwaters and especially seawater, ionic strength is likely to be a poor predictor of the effect ions such as Ca2+and Mg2+may have on the electrostatics of oligoelectrolytes in the solution. In the case of the penetrable sphere, the relevant charge parameter is pot the charge density contained in the volume of the sphere in the absence of counterions. Figure 2 shows the model results for this geometry, analogous to Figure 1 of the impenetrable sphere model. In this case = exp(-(e*av/kT)) (11) where \kav is an average of \k(r) over the volume of the humic phase: \kav = LR(3r2/R3)yI(r)dr

(12)

Despite the fact that this averaging of \k is strictly correct only when \k is small (and the exponential can be linearized) it turns out to give a reasonable “average A” in all cases because when \k is large it is almost constant over Environ. Sci. Technol., Vol. 26, No. 2, 1992 287

Table 11. Comparison of Electrostatic Factors log A" 109

R = 3 A, 2 = 1 (a) (b) (C)

R = 9 A, 2 = 1 (a) (b)

(4

x

I = 0.1 M

I = 0.01 M

I = 0.00E

0.79 0.77

0.94

0.93

0.89

1.1

1.0 0.99 1.1

0.18

0.27

0.18

0.26 0.32

0.20

0.32 0.31 0.35

Derived from (a) a linearized Poisson-Boltzmann equation of an impenetrable sphere (essentially the Debye-Huckel model, but without correction for the electrostatic potential at the limit of zero ionic strength; see Appendix); (b) nonlinear Poisson-Boltzmann equation of an impenetrable sphere (numerical solution); (c) nonlinear Poisson-Boltzmann equation of a penetrable sphere (numerical solution). (I

the volume of the phase (i.e., Q approaches a step function). As discussed in the Appendix, this definition of 9, is formally correct if X is considered to be a work function instead of a concentration factor. We can again describe the results of the numerical calculations with a three-parameter equation: p o = a sinh ( b log X) + c (log X) (13) However, instead of optimizing the fit, as we did for the impenetrable sphere, we used our knowledge of the limiting behaviors of the solution to estimate the parameters a, b, and c. When pa and log X are small, log X is a linear function of po, its slope predicted by the analytical solution for this geometry found in Tanford (18). When po and log h become very large, the numerical solution behaves like the Donnan model, which simply says that X = - p o / l (if X >> 1). The function above displays the required behavior when a = 21, b = In 10, and l / ( c ab) is equal to the slope (log X ) / p o given by the Tanford model (which can be calculated directly given R and I). With these directly calculated parameters, we obtained good approximations to the numerical solution at ionic strengths of 0.1, 0.01, and 0.001 M, radii of 5, 10, 20, 40, and 100R and charge densities po from 0 to 5 M. Equation 13 and the numerical solutions agreed within 0.1 log unit, in all but two cases. At a radius of 10 A, ionic strengths 0.01 and 0.001 M, and charge densities above 3 M, the approximation deviates from the solution by as much as 0.15 log unit (27). Using the same charge density parameters that we used in the impenetrable sphere model, we find that a radius of 7.7 A and a molecular mass of 711 Da correspond to a charge density po of 3.7 M inside the humic phase. Since total charge and volume are both proportional to R3,in this model the charge parameter is a constant for all size groups. Nevertheless, the effect of size on log X is substantial in the size range of interest (5-20 A). Figure 2 shows this effect as well as the asymptotic behavior of the function-approaching the Tanford (linearized) model when log X is small and the Donnan model when X is large. Note that once the molecule is large enough to be well described by the Donnan model ( R > 30 A or so), there is no longer a size effect on A. Also, the effect of ionic strength on X is once again no larger than proportional. Finally, despite the difference in the physical picture, the results of the penetrable sphere model for small molecules agree closely with those predicted for the impenetrable sphere (Debye-Huckel) model (Table 11). Both the penetrable and impenetrable sphere models can describe the effect of size distributions elegantly and

+

288


provide an "in-between" solution for oligoelectrolyte molecules not described well by either Debye-Huckel or polyelectrolyte models. Their behavior converges on a Debye-Huckel-type behavior for small-sized molecules (Table 11), and on either the Donnan model (penetrable spheres) or the Gouy-Chapman model (impenetrable spheres) when the radius becomes very large. The choice between penetrable and impenetrable sphere models is at this point somewhat arbitrary. We have chosen to use an impenetrable sphere model because in this model the thorny issue of appropriate intramolecular dielectric constant can be ignored, and because it presents a more reasonable physical picture of small molecules. The assumption that the surface charge density u increases proportionally to R-i.e., the carboxylic content is proportional to weight-may, however, be inappropriate for molecules much larger than 20 A. The seemingly very different types of electrostatic models discussed above are all indistinguishable from each other in some sense. The predicted absolute values of X, and the amount of neutralization of polyion charge by counterions, vary from model to model, but if we have no a priori information concerning the magnitude of intrinsic binding constants, the observation that X is proportional to 1/I or that the apparent acidity constant is proportional to I for some reaction does not alone suffice to let us distinguish among models. In fact the Donnan model and all of the nonlinear Poisson-Boltzmann models exhibit this behavior, first discussed in relation to Manning's model: that X is proportional to 1/1in some ionic strength range and at sufficiently high charge densities, so that the local concentration of counterions does not vary with ionic strength. There is one important difference between planar, cylindrical, and spherical geometries. For the first two (and the penetrable sphere), this "condensation" behavior continues in the limit of low ionic strength, so that X approaches infinity in this limit. In the case of the impenetrable sphere, however, X approaches a finite value, calculated by setting '7% equal to zero in eq 1. However, Zimm and LeBret (23) pointed out that the actual differences are very small above 0.001 M ionic strength (the only condition relevant to most laboratory or natural systems). Our results, then, are not highly dependent on the specific geometry we choose to describe a humic acid, nor can positive results in our modeling efforts be construed as "proof" that the molecule looks more like a sphere than a plane. What is important is that a model has been chosen that is appropriate for an oligoelectrolyte, that can handle size distributions, and that can easily be incorporated into existing computer programs for speciation calculations.

Modeling Now that we have chosen a model and explored its basic characteristics, we can study the data sets and ask ourselves whether or not our chosen model is able to explain the observed effects. We want our model to exhibit the strong pH and ionic strength effects on titrations of Suwannee River fulvic acid with Cu2+(Figure 3) measured by Cabaniss (31),while at the same time showing the small ionic strength effect observed in pH titrations (Figure 4). Our computational techniques have been adapted from the diffuse layer model version of Westall's BASIC computer program MICR~QL (32). In addition to copper-fulvate complexes, the inorganic species Cu(OH)+and CU(OH)~ were included in the equilibrium calculations, using the formation constants compiled in Morel (33). Inorganic complexes of copper with the buffer ions (1 mM PO4 in the pH 7.00 titrations and 1 mM C03 in the pH 8.44 ti-

-101

L

,

.,

Flgure 3. Cu2+ titration data collected by Cabaniss (31). The plot shows pCu vs pCu, (concentration scales) at three different pH's and two ionic strengths in the presence of 5 mg of C/L Suwannee River fulvic acld.

of magnitude) at pH 8.44; (6) the large pH effect at ionic strength 0.1 M (at low CuT, 1.6 log units as pH varies from 5.14 to 7.00, and also 1.6 log units as pH varies from 7.00 to 8.44); (6) varying pH effects at ionic strength 0.01 M (at low CUT,3.0 log units as pH varies from 5.14 to 7.00 and only 0.9 log unit as pH varies from 7.00 to 8.44). We use a combination of discrete binding sites instead of continuous distributions chiefly for calculational and conceptual simplicity in dealing with proton-exchange stoichiometries for which no parallel exists in continuous distribution models. Our discrete ligand models allows us to understand how the electrostatic factor X relates to pH and ionic strength effects, by considering how an apparent copper binding constant may be formulated under different conditions. For a diprotic site, three cases are possible: binding copper to the site may release two protons, one proton, or no proton, depending on the acidity constants of the site and the pH of the solution. This leads to three possible expressions for the apparent binding strength (at low copper loading) KCu,app:

10 0

F

8

L

e,

a

-l 6 a Y

?i4 0

04 4

5

6

I=O.l M

A

I = 0.01 M I = 0.001 M

7

a

0

I

9

PH Flgure 4. Titrations of 400 f 2 g/L Lake Drummond fulvic acid with 0.100 f 0.001 M NaOH performed in covered Teflon beakers under flowing nitrogen. pH measured by Orion EA 920 voltmeter and a Ross combination pH electrode at 22-24 OC, with 2-4 min Intervals between base addition and measurement. Activity coefficients from Kielland (38)used to calculate [H'].

trations) were found to be insignificant. Precipitation of solids was not considered although, at high pH, the solution was calculated to be supersaturated with Cu(OH),(s) at copper concentrations up to a factor of 10 lower than those at which Cabaniss (31) could detect the presence of precipitates and stopped the titration. In the modeling that follows, pCu and PCUT refer to -log [CU"] and -log [CuT] (concentration scales), while pH refers to -log { H'} (activity scale). Solution activity coefficients were estimated using the Davies equation with A = -1.17 and b = 0.24 (33). Our forward modeling approach consists of beginning with an oversimplified model (one size group, one acidic site, and one copper binding site) and exploring how closely we can fit the data by varying the model's parameters. We then consider how the model fails and why, and add complexity stepwise, reasoning at each step how the next level of complexity should improve the fit (Figures 5a-c and 6a-c). Our goal is not an optimized fit of the data set but a concise explanation of the observed pH and ionic strength effects. The features of Figure 3 to be explained are as follows: (1)the general "smeared" appearance of the curves (slope of pCu vs pCuT = 2 over 1.5 orders of magnitude); (2) the lack of binding and the small ionic strength effect at pH 5.14; (3) the very large ionic strength effect (almost 2 orders of magnitude for a 10-fold change in ionic strength) at pH 7; (4) a smaller ionic strength effect (approximately 1order

where KCaint, Kalht,and Kaz,intare intrinsic copper binding and acidity constants of the site, expressed in terms of "local" concentrations of solution ions, and pH is the local pH, given by pH - log X (see eq 5). In other words, when the site is more deprotonated, competition with H+ becomes less of a factor since fewer protons are exchanged in the reaction, but the electrostatic factor X becomes more significant since more charge is exchanged. Thus, one might expect the ionic strength effect to increase and the pH effect to decrease with increasing pH. This expected result occurs in the modeling attempt shown in Figure 5a. To construct this model, we assumed that carboxylic acids are the prevalent acidic sites and that two carboxylic acids in close proximity to each other (such as a malonic acid) are the prevalent copper binding sites. K,'s and Kcu's were chosen to reflect this assumption (Table 111); total ligand concentrations are consistent with the titrimetric measurements of Bowles et al. (30)and the spectrometric measurements of Noyes and Leenheer (34), who measured total carboxyl contents of Suwannee River fulvic acid at 6.1 and 6.8 mequiv/g, respectively. To keep the model simple, the monoprotic acid site was assumed to create charge density only and not to affect the copper binding (although at the high copper loadings characteristic of some data sets, a weak site such as acetate or benzoate could play a significant role). Figure 5a demonstrates that this one-site model has other flaws besides its expected inability to produce the pH and ionic strength effects observed in the data. The titrations are not "smeared", reflecting the fact that only one binding site dominates the binding. To see reasonably large ionic strength effects, a molecular weight much larger than the measured averages had to be used. Finally, a pH titration of the same model (Figure 6a) shows large ionic strength effects. Like the pH and ionic strength effects on copper titrations, this was also to be expected. The largest effect electrostatics can have on KCu,app is a factor of A', while the smallest effect we would see on the Ka,ap is a factor of A. To model the ionic strength effect at p d Environ. Sci. Technol., Vol. 26, No. 2, 1992

289

12 10 0

L

0

n

- 6

sI I

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4

*-.

I

2 -7

-5

-6

-4

5

6

0.1 Y

I

.-a

-4

lOdCLJT1

-I

0-0

-

0.01

u

0.001 Y

s

7

9

PH

12 10 0

F a

k

n

sI

6

9 4

e-.

2 -121 -7

-6

-5

-4

lOdC~T1

0 4

I

--

0.1 Y

.-. -

0-0

5

6

I

0.01 Y

I

0.031 Y

7

8

7

8

PH

-124 -7

-6

m[cLJ,l

-5

I

-4

Flgure 5. Model results of copper titration data at ionic strengths 0.01 and 0.1 M at pH's 5.14, 7.00, and 8.44. Symbols represent the data shown in Figure 3. Fits use an impenetrable sphere model with the size to charge density relationship used in Figure 1. (a) Attempt at fitting the data b use of one copper binding site and one size group (radius R = 15 molecular mass 5260 Da), using equilibrium constants and total ligand concentrations shown in Table 111. An addltbnal acidic (but not copper binding) site dominates the electrostatics. (b) Model resub using one copper binding site, one acidic slte (see Table 111), and two size groups: R = 7.7 A, molecular mass 71 1 Da, 75% by weight; R = 15 A, molecular mass 5260 Da, 25% by weight. (c) Model results using two copper binding sites, one acidic slte (Table HI), and the same two size groups used in Figure 5b.

1,

7, we need X to increase by a factor of -10 as the ionic strength is decreased from 0.1 to 0.01 M-and this factor of 10 produces significant effects indeed on the pH titration (which is on a linear scale). Note also that according to our conclusions of the previous section, the factor of 10 is the largest possible ionic strength effect on A. In the context of Poisson-Boltzmann models, there is only one way that the electrostatics could have such a large effect on Cu titrations and such a small one on pH titrations: the fulvic acid must be a mixture of substances with different electrostatic properties, one of which dominates the H+ binding and the other the Cu2+ binding. This situation is most simply and logically produced by using 290


4

5

6

9

PH Flgure 6 . (a-c) Ionic strength effect on a model pH titration, using the same model parameters as in Figure 5a-c, respectively. The total concentration of dissociated acidic sites in the solution, represented as [A-1, is given by [OH-],,& - [OH-] -t [H'].

a size distribution of molecules. As shown below, even if the content (per weight) of acidic and copper binding sites remains constant from one molecular size to another, a small amount of large molecules with large values of X can dominate the Cu2+ binding while a larger amount of smaller molecules with a small X will dominate pH titrations. Figures 5b and 6b were produced using a mixture of two size groups. The ratio of molecular weights used produces a polydispersity of 2.0, within the range of the measurements of Beckett et al. (13). In addition, the numberaverage molecular weight is now 907, in closer agreement with the measurements, and the Cu2+titrations appear more smeared than in Figure 5a, because the same copper binding site distributed among two size groups behaves like two sites of different strengths and concentrations. However, introducing two size groups has not solved the problem of pH and ionic strength effects. We can greatly improve our model fit by simply introducing another

Table 111. Total Ligand Concentrations (per 5 mg of C/L), Intrinsic Equilibrium Constants, and Literature Constants of the Binding Sites Used in the Modeling Work” “acetate”

”malonate”

“catechol”

model

PKa

~

L

T PKa1

PKaz

PKC~

~

L

Figures 718 Figures 9/10 Figures 11/12 literature constants corrected lit. constants high low

3.8 3.8 3.8

-4.40 -4.40 -4.40 4.76

4.5 4.5 4.5 2.85

4.5 4.5 4.5 5.70

4.5 5.1 5.1 5.70

-5.00 -5.00 -5.00

4.57 4.24

2.66 2.33

5.13 4.14

4.94 3.62

TP K ~ I

PKaz

PKC~

~

L

9.40 9.40

12.60 13.44

14.68 14.78

-5.28

9.21 8.88

12.87 11.88

14.02 12.70

T

a Where two size classes are present, the total amount of ligand in each size class is determined by the weight fraction of that size class. Literature constants were taken from Morel (33). Catechol constants are from Martell and Smith (37), corrected for ionic strength as in Morel (33). A possible range of constants corrected for the difference in reference state between literature constants and the intrinsic constants of this model is derived as described in the Amendix.

binding site. Examination of Figure 5b suggests that the titration most out of place is the one at pH 8.44 and ionic strength 0.1 M. Introducing a binding site which becomes significant only under these conditions may solve the problem. A diprotic site such as catechol does not significantly deprotonate in the pH range of interest. Its apparent binding constant is hence governed by eq 14a. When incorporating this new type of site into our model, we are again guided by the titrimetric data of Bowles et al. (30) and the spectromeitric data of Noyes and Leenheer (34),reporting phenolic OH contents in Suwannee River fulvic acids of 1.2 and 1.4 mequiv/g (“reactive” phenolic OH), respectively. Our chosen value of 0.53 mM/g catechol content is not incompatible with these figures, although it suggests that almost all of the phenolic sites participate in Cu binding. When a site of this kind is added to the model, its behavior is much closer to that exhibited by the data (Figure 5c), while the pH titration (Figure 6c) remains unaffected. However, the copper titrations at high pH become sharp again instead of smeared. Since the Kcu,a of the diprotic site dominating at this pH is not affected f ~ yh (see eq 14a), the two size groups do not appear as two sites of apparently different strengths. A third binding site, which again only becomes significant at high pH’s, may be needed to produce the smearing. Although we could add more binding sites or size groups to smooth out Figure 5c a bit, the two-site, two-size group model does meet our initial requirement of explaining the major pH and ionic strength effects on copper titrations concisely. Relative ionic strength effects on pH titrations are also explained adequately by this model (compare Figures 4 and 6c). A better fit of th.e Lake Drummond fulvic acid titration can be obtained by lowering the total concentration of acidic sites from 12 to 10 pM/mg of C and adding another strong acidic site (Figure 7).

Discussion According to our results, size heterogeneity in humic substances is not significant for modeling pH titrations which are dominated by the more numerous smaller molecules. In this respect our model is similar to those recently published by DeVVit et al. (9) and Tipping et al. (IO),which both use impenetrable spheres of a single size. After correction by the appropriate nonlinear Coulombic term, DeWit et al. (9) interpreted their result with a continuous distribution of acidity constants rather than discrete values. Tipping et al. (IO)used a discrete site model and calculated their Coulombic corrections with the linear approximation of the Poisson-Boltzman equation. Except perhaps at high pH where the potentials are larger, this is an adequate approximation for oligoelectrolytes of size

12

2t

04 4

5

7

6

8

I

PH Figure 7. Model pH titration using the same size dlstriblRion as Figures 5b and 6b and the following binding sites (compare to Table 111): strong acid, pKa 2.5, log L T-4.76; “acetate”, pKa 3.8, log L T-4.76; “malonate”, pK, 4.5, pKa2 4.5, log L , -5.06. Total ligand concentrations are given for 5 mg of C/L. I n this model the total acidity mequiv/g of C instead of 12 X content is 10.5 X mequiv/g of c.

6.4 A and a charge number 6. This linear approximation is, however, inappropriate for larger sizes and Tipping et al.’s discussion of how to handle size heterogeneity is accordingly flawed. In order to deal with the issue of metal binding in the context of their model with a continuous distribution of pKa)s, DeWit et al. (9) had to resort to defining extreme cases of coupling or uncoupling of metal and proton coordination to humates. (Other works (5, 35) make no attempt to explain metal and hydrogen ion titrations within a single model.) Even if one could satisfactorily handle the issue of the acidity of metal binding sites in this manner, this approach misses the role that size heterogeneity plays in humic binding. If proton and metal binding are dominated by different size fractions (and this seems to be the only way to explain the data sets), it is futile to try to apply electrostatic information extracted from a pH titration (such as conclusions about size and charge of molecules) to a metal titration. To measure the conciseness of our model, we can count the number of fitting parameters used: 7 equilibrium constants (two Kc,’s and five Ka’s, three total ligand concentrations, and four size parameters (the two radii, the concentration ratio of large to s m d molecules, and one parameter describing the size to charge density relationship), for a total of 14. However, if we consider that the two pK,’s of the catechol-type site are arbitrary as long as they are much greater than 8.5, and that we used measured values of total carboxylic acid content, one radius, and the size to charge density relationship, we can reduce the number of fitting parameters to nine. FurEnviron. Sci. Technol., Vol. 26, No. 2, 1992

291

thermore, the other size parameters and the total concentration of catechol-type sites are also limited by measurable quantities (polydispersity and total phenol content). In comparison, Cabaniss and Shuman’s 5 binding site model (3) uses a total of 15 parameters: 5 unconstrained Kc;s and total ligand concentrations, and five “protonicities” (which could only take on values of 0, 1, or 2). Although our oligoelectrolytemodel is not yet developed sufficiently to predict metal speciation in the presence of DOC in natural waters, it does allow us to gain some chemical insights into effects we might observe and also suggests a need for certain kinds of data sets. For example, surprisingly little data showing large ionic strength effects on metal-humate binding have been published; we predict that further experiments under the right conditions will confirm Cabaniss’ results (31). The belief that ionic strength effects are in general not large still prevails, despite the evidence to the contrary. One reason for this is that, at the conditions of high metal loading studied in most cases, the more abundant monoprotic weak binding sites (such as acetate) on the smaller molecules are dominating the binding. In this case, the ionic strength effect must be similar to that observed in the pH titrations and could easily be described by Debye-Huckel activity coefficients, as shown by Susetyo et al. (35). Since the “right” conditions for seeing large ionic strength effects are also the conditions most likely found in natural waters, more studies need to be carried out at low metal loading. Another prevalent condition in natural waters is the presence of competing metal ions. Some studies have been done to examine for example the effect of ea2+,Mg2+,or Cd2+on copper ion binding by fulvic acid (see refs 3, 4, and 36). However, these were carried out at one pH and ionic strength only. Our model suggests that competition effects may differ widely depending on which type of site dominates the binding under the conditions examined. A data set comparing metal binding competition in a range of ionic strength and pH conditions would provide some valuable insights into these issues.

Conclusions We have shown that the nonlinear Poisson-Boltzmann equation of an impenetrable sphere is an appropriate oligoelectrolyte model for a fulvic acid molecule. Two size groups of molecules, two kinds of copper binding sites with different proton-exchange stoichiometries, and one additional acidic site are sufficient to explain some nonintuitive ionic strength effects observed in the data. In particular, the relatively small effect of ionic strength on pH titrations, as compared to Cu titrations, is logically explained by the dominance of the more abundant small molecules in the former and the importance of relatively few large molecules in the latter. In such a situation, one clearly cannot extrapolate information about electrostatic effects extracted from a pH titration to a metal titration or vice versa. We are encouraged by the success of this simple chemical model. By keeping the physical picture uncomplicated and incorporating a variety of available data concerning molecular weight distribution, size, and functional group content of humic substances, we can minimize the number of arbitrary fitting parameters and also gain some chemical information. For example, our results suggest that OXYgen-containing binding sites, with their binding strengths enhanced by an electrostatic effect, are sufficient to explain the extent of Cu binding in the range of copper-humate ratios that have been studied, without invoking unknown strong ligands. Furthermore, irreversible effects such as size changes (“unfolding”) or esterification need not be 292


invoked to explain “strange” shifts in titrimetric data at high pH. There appears to be an evolving concensus to model humic acids as impenetrable spherical oligoelectrolytes. As this model evolves into a predictive one, we note that site heterogeneity is likely to be a much more important fador in the modeling of divalent metal ion titrations than has previously been considered, especially under conditions of low metal loading. Appendix This appendix addresses some of the fundamental thermodynamic issues behind the use of the PoissonBoltzmann equation to calculate solution activity coefficients. In the main body of this paper, we have used the idea of a “local” concentration of metal ion near the charged polyions, [Mz+] = XZ[MZ+],to derive expressions for the electrostatic effect on the apparent equlibrium constants of metal-polyion reactions. Although this is an intuitively pleasing mental construct, we would like to show here that the electrostatic factor X can also be interpreted as a ratio of polyion activities. This more rigorous approach emphasizes our models’ formal similarity to the Debye-Huckel model. Debye-Huckel activity coefficients for ions in electrolyte solutions are calculated from the work required to bring a solution ion from a hypothetical uncharged state to its charge &e, by assuming that with each infinitesimal increase in charge dq the ions surrounding the ion of interest rearrange themselves in the resulting potential field according to the Poisson-Boltzmann equation. The work is calculated from the Poisson-Boltzmann potential at the surface of the central ion (Qo):

If We, is the only nonchemical contribution to the free energy of the system, and the linear approximation to the Poisson-Boltzmann equation (which results in a \k, that is a linear function of charge) is valid, the activity coefficient of the central ion is In yg = W,,/kT = Qe\ko(Qe)/2kT (A.2) The oligoelectrolyte models discussed in the text also calculate We,as an integral of the Poisson-Boltzmann potential, eq A.l for an impenetrable sphere and

for a penetrable sphere, where the inner integral sums the work required to charge each spherical shell of thickness dr over the total volume of the sphere (18). However, for a polyion, eq A.2 may no longer be valid since the linear approximation is expected to fail when the charge density is large. Consider a reaction between a polyion of charge Q- and a small ion of charge Z+: AQ- + MZ+-+ A-MZ-Q (-4.4) The apparent (conditional) equilibrium constant for this reaction is Kapp

=

[A-Mz-Q] - (A-Mz-Q) YQYZ -[AQ-][Mz+] (A@){Mz+) YZ-Q

YQ - KintYz-72-Q

(A.5) Thus, it is the ratio of polyion activity coefficients YQ/yz-g and the simple Debye-Huckel activity coefficient for the small ion that will appear as the corrections to Kintin the

equilibrium expression. One could define a “localnmetal ion activity coefficient (a surface to bulk concentration ratio):

be compared to Klit, but to the literature constant “correctedn for high ionic strength conditions. Kcom = Klit(YQ/YQ+Z) (A.12)

In

Debye-Huckel activity coefficients for an ion of charge q (see, for example, ref 33) are given by log yq = 0.434 Aq2[11/2/(1 + B u ~ / ~ )(A.13) ]

Teff

= In (YQ/YZ-Q) =

impenetrable sphere (A.6)

In yg - In yZ-Q

=

2

&e(z-Q)e(

lR

$Q(r,q) dr

dq

penetrable sphere (A.7)

If Q is much larger than 2, @,(q) and \k(r,q) remain approximately constant over the range of the integral, so that

Ze kT

impenetrable sphere (A.8)

Teff = -.-@(&e)

1 R

=-

;:(r,Qe)

dr

penetrable sphere

(A.9)

Thus Teff equals Xz as defined by eqs 9 and 11 in the text as long as the charge of the polyion does not come close to being neutralized by the reaction. This alternative picture of a “local”activity of the solution ion at the surface of the polyion or within the polyion phase (see eq 5) is valid whenever eq A.8 and A.9 are. So far, we have shown that the differences between our formulation of activity coefficients and the Debye-Huckel equation are minor: we do not use a linear approximation (since it is no longer appropriate), and we express the ratio of two activity coefficients as an effective coefficient, leading to the correction factor log A. The remaining important difference is the reference state for the binding constant (zero ionic strength vs zero potential). @, in eq A . l has a finite value at zero ionic strength, but the Debye-Huckel approach includes this contribution to We,in the “intrinsic” binding constant, giving activity coefficients of exactly 1 at ionic strength zero. The approach used here does not “subtract outn this contribution so that the reference state (log X = 0) for the polyion is the condition where \k, is actually zero. This difference in reference state affects only the absolute magnitude of the activity coefficients (and therefore the magnitudes of the intrinsic binding constants) and not the relative effects of ionic strength. However, if we are concerned with comparing the magnitudes of the intrinsic binding constants (the fitting parameters of our model, K.,J with magnitudes of literature constants (Kbt)we need to have a common reference state, either zero ionic strength or zero potential. Consider a binding site (with literature binding constant KliJ attached to a larger charged molecule. Assume that the only effect of this attachment on the binding strength is the Coulombic effect of the other charges. The apparent binding constant (Kapp)of the attached site should be independent of these charges when the potential is zero or a t sufficiently high ionic strength. In this case, yQand yQ+zare equal to 1 and eq A.6 reduces to Kapp

= KintYz

(A. 10)

where 2 is the charge of the small ion. For the binding site alone (not attached to a polyion) Kapp = Klit(YQYZ/YZ-Q) (A.11) where Q in this case is the charge of the binding site alone, and all y’s are Debye-Huckel activity coefficients. Comparing these two equations, we can see that Kht should not

where A and B are constants (1.17 and 0.328, respectively) and a is the radius (in angstroms) on the ion. The mathematical limit of the activity coefficient as ionic strength approaches infinity is log YQ = -1.55(q2/a) (A.14)

For example, in the case of an acidity constant, Q = -1 and Q + 2 = 0, leading to log YQ = -1.55/1 and log YQ+Z = 0. The size parameter a lies in the range of 3-8 A for common organic acids (38), leading to a corrected pK, that is 0.19-0.52 log unit lower than the literature constant. Similarly, the copper binding constants tabulated in Table I11 must be corrected by 0.76-2.08 log units. The idea of a binding constant simultaneously incorporating two reference states (as is the case for our intrinsic Rs)may seem unnecessarily complicated. In the case of the impenetrable sphere model, it would in fact be trivial to define constants that use zero ionic strength as a reference state. However, this is impossible for other geometries, infinite planes and cylinders, for which the surface potential approaches infinity as the ionic strength approaches zero. It is for the sake of consistency with other polyelectrolyte models that we use zero potential as a reference state. Registry No. Cu, 7440-50-8. Literature Cited Perdue, E. M.; Lytle, C. R. In Aquatic and Terrestrial Humic Materials; Christman, R. F., Gjessing, E. T., Eds.; Ann Arbor Science: Ann Arbor, MI, 1983; Chapter 14. Dzombak, D. A,; Fish, W.; Morel, F. M. M. Environ. Sci. Technol. 1986,20, 669-675. Cabaniss, S. E.; Shuman, M. S. Geochim. Cosmochim.Acta 1988,52, 185-193. Fish, W. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1984. Grimm, D. M.; Azarraga, L. V.; Carreira, L. A,; Susetyo, W. Environ. Sei. Technol. 1991, 25, 1427-1431. Tipping, E.; Hurley, M. A. J . Soil Sei. 1988, 39, 505-519. Ephraim, J.; Marinsky, J. A. Environ. Sei. Technol. 1986, 20, 367-376. Green, S. A.; Morel, F. M. M.; Blough, N. V. Environ. Sci. Technol., following article in this issue. DeWit, J. C. M.; Van Riemsdijk, W. H.; Nederlof, M. M.; Kinniburgh, D. G.; Koopal, L. K. Anal. Chim. Acta 1990, 232, 189-207. Tipping, E.; Reddy, M. M.; Hurley, M. A. Environ. Sci. Technol. 1990,24, 1700-1705. Aiken, G. R.; Malcolm, R. L. Geochim. Cosmochim.Acta 1987,51, 2177-2184. Aiken, G. R.; Brown, P. A.; Noyes, T. I.; Pinckney, D. J. in Humic Substances in the Suwannee River, Georgia: Interactions,Properties,and Proposed Structures;Averett, R. C.; Leenheer, J. A., McKnight, D. M., Thorn, K. A., Eds. Open-File Rep.-U.S. Geol. Suru. 1989, No. 87-557, 163-178. Beckett, R.; Zue, Z.; Giddings, J. C. Environ. Sci. Technol. 1987,21, 289-295. LeBret, M.; Zimm, B. H. Biopolymers 1984,23, 271-285. Kirkwood, J. G. J. Chem. Phys. 1934,2, 767-781. Fixmann, M. J. Chem. Phys. 1979, 70, 4995-5005. Debye, P.; Huckel, E. Phys. 2. 1923,24, 185. Tanford, C. Physical Chemistry of Macromolecules;Wiley: New York, 1961; pp 457-472. Environ. Scl. Technol., Vol. 26, No. 2, 1992 293

Environ. Sci. Technol. 1992, 26, 294-302

Wershaw, R. L.; Pinckney, D. J. J. Res. U S . Geol. Suru. 1973, I , 701-707. Verwey, E. J. W.; Overbeek, J. Th. G. Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948. Dzombak, D. A.; Morel, F. M. M. Surface Complexation Modeling: Hydrous Ferric Oxide; Wiley: New York, 1990. Manning, G. S. Acc. Chem. Res. 1979, 12, 443-449. Zimm, B. H.; LeBret, M. J. Biomol. Struct. Dyn. 1983, I , 461-471. Kotin, L.; Nagasawa, M. J. Chem. Phys. 1962,36,873-879. Delville, A. Chem. Phys. Lett. 1980, 69, 386-388. Mandel, M. In Encyclopedia of Polymer Science and Engineering; Mark, H. F., Bikales, N. M., Overberger, C. G.; Menges, G., Eds.; Wiley: New York, 1988; Vol. 11, pp 739-829. Bartschat, B. M. M.S. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1990. Muller, H. Kolloidchem. Beih. 1928, 26, 257-310. Wall, F. T.; Berkowitz, J. J. Chem. Phys. 1957,26,114-122. Bowles, E. C.; Antweiler, R. C.; MacCarthey, P. In Humic Substances in the Suwannee River, Georgia: Interactions, Properties, and Proposed Structures; Averett, R. C., Leenheer, J. A., McKnight, D. M., Thorn, K. A. Eds. Open-File R e p . 4 J . S . Geol. Surv. 1989, No. 87-557, 205-229.

(31) Cabaniss, S. E. Ph.D. Thesis, University of North Carolina, Chapel Hill, 1986. (32) Westall, J. c. MICROQL 11. Computation of Adsorption Equilibria in BASIC. Technical Report, Swiss Federal Institute of Technology, EAWAG: Dubendorf, Switzerland, 1979. (33) Morel, F. M. M. Principles of Aquatic Chemistry; Wiley: New York, 1983. (34) Noyes, T. I.; Leenheer, J. A. In Humic Substances in the Suwannee River, Georgia: Interactions, Properties, and Proposed Structures; Averett, R. C., Leenheer, J. A., McKnight, D. M., Thorn, K. A., Eds. Open-File Rep.-U.S. Geol. Suru. 1989, No. 87-557, 231-250. (35) Susetyo, W.; Dobbs, J. C.; Carreira, L. A,; Azarraga, L. V.; Grimm, D. M. Anal. Chem. 1990,62, 1215-1221. (36) Hering, J. G.; Morel, F. M. M. Environ. Sei. Technol. 1988, 22, 1234-1237. (37) Martell, A. E.; Smith, R. M. Critical Stability Constants; Plenum: New York, 1977; Vol. 111, pp 200-201. (38) Kielland, J. J. A m . Chem. SOC.1937, 59, 1675-1678.

Received for review February 25, 1991. Revised manuscript received October 14,1991. Accepted October 23,1991. This work was supported in part by Grants R817371-01-0 f r o m E P A and OCE-9116427 from N S F .

Investigation of the Electrostatic Properties of Humic Substances by Fluorescence Quenching Sarah A. Green,*,+Franqois M. M. Morel,*,$and Neil V. Blough*!§ Department of Chemistry, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, and Ralph M. Parsons Laboratory, Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02 139

A fluorescence quenching technique was employed to explore the electrostatic properties of fulvic acid (FA) and humic acid (HA). Cationic nitroxides were found to be up to 16 times more effective than neutral analogues in quenching the fluorescence of humic materials. This result is attributed to the enhanced Coulombic attraction of cations to the anionic FA or HA surface and is interpreted as an estimate of surface potential. Reduction of molecular charge at low pH and shielding of charge at high ionic strength produced diminished enhancements, consistent with this interpretation. High molecular weight fractions of HA have a higher apparent surface potential than lower molecular weight fractions, indicating that larger humic molecules may have an enhanced ability to bind metal ions. Introduction Humic substances play an important role in controlling trace-metal speciation in natural waters. As the prevalent chromophores in most aquatic environments, they are also responsible for initiating numerous photochemical transformations of both organic compounds (1, 2) and trace metals ( 3 ) . With the goal of better understanding these processes, a great deal of effort has gone toward modeling the interactions between metal ions and humic materials ( 4 , 5). Recently the electrolyte character of fulvic acids and humic acids has been considered in terms of its impacts on both cation binding (6, 7) and rates of photochemical reactions (8). Joint Program in Oceanography. Institute of Technology. 5 Woods Hole Oceanographic Institution. t MIT-WHO1

t Massachusetts

294


A current approach to modeling metal binding by humic acids over variable pH and ionic strength regimes explicitly includes a Coulombic term in addition to intrinsic binding constants (6, 7 , 9 , 1 0 ) .In these models, intrinsic binding constants remain invariant with pH and ionic strength while the Coulombic term is allowed to vary as predicted by electrostatic theory. Initial application of this type of model has been successful in this laboratory (6) in fitting copper titration data without relying on such physically unsatisfying concepts as binding constants that vary with ionic strength. Natural humic substances are oligoelectrolytes which are predicted to have a large negative surface potential, primarily due to deprotonated carboxylic acid groups. This negative potential is expected to result in increased cation concentrations near the humic surface. Experimentally this has been confirmed indirectly by Blough (8), who has shown that radicals produced by irradiation of humic acid are more efficiently scavenged by a cationic species than by analogous neutral or anionic compounds. Thus, electrostatic effects can influence the competition between charged and neutral species (e.g., oxygen) for photoproduced radicals. Similarly, this region of enhanced cation concentration around humic molecules may be an important zone for thermal and photoinduced metal reduction/oxidation, since an ion here may be sufficiently close to act as an electron acceptor/donor, yet be able to diffuse away before undergoing back electron transfer. In this work our goal is to provide an experimental basis for models that require information about the electrostatic characteristics of humic materials. We have employed a fluorescence quenching technique to explicitly examine the local excess of cations around fulvic acid molecules and

0013-936X/92/0926-0294$03.00/0

0 1992 American Chemical Society

Oligoelectrolyte model for cation binding by humic substances

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